Arrays can have a compile-time fixed size, or they can have a dynamic size.

The type of an array of fixed size k and element type T is written as T[k], and an array of dynamic size as T[].

For example, an array of 5 dynamic arrays of uint is written as uint[][5].
The notation is reversed compared to some other languages.
In Solidity, X[3] is always an array containing three elements of type X, even if X is itself an array.
This is not the case in other languages such as C.

Indices are zero-based, and access is in the opposite direction of the declaration.

For example, if you have a variable uint[][5] memory x, you access the seventh uint in the third dynamic array using x[2][6], and to access the third dynamic array, use x[2].
Again, if you have an array T[5] a for a type T that can also be an array, then a[2] always has type T.

Array elements can be of any type, including mapping or struct. The general restrictions for types apply, in that mappings can only be stored in the storage data location and publicly-visible functions need parameters that are ABI types.

It is possible to mark state variable arrays public and have Solidity create a getter. The numeric index becomes a required parameter for the getter.

Accessing an array past its end causes a failing assertion. Methods .push() and .push(value) can be used to append a new element at the end of a dynamically-sized array, where .push() appends a zero-initialized element and returns a reference to it.

Variables of type bytes and string are special arrays.
The bytes type is similar to bytes1[], but it is packed tightly in calldata and memory.
string is equal to bytes but does not allow length or index access.

Solidity does not have string manipulation functions, but there are third-party string libraries. You can also compare two strings by their keccak256-hash using keccak256(abi.encodePacked(s1)) == keccak256(abi.encodePacked(s2)) and concatenate two strings using string.concat(s1, s2).

You should use bytes over bytes1[] because it is cheaper, since using bytes1[] in memory adds 31 padding bytes between the elements.
Note that in storage, the padding is absent due to tight packing, see bytes and string.
As a general rule, use bytes for arbitrary-length raw byte data and string for arbitrary-length string (UTF-8) data.
If you can limit the length to a certain number of bytes, always use one of the value types bytes1 to bytes32 because they are much cheaper.

You can concatenate an arbitrary number of string values using string.concat.
The function returns a single string memory array that contains the contents of the arguments without padding.
If you want to use parameters of other types that are not implicitly convertible to string, you need to convert them to string first.

Analogously, the bytes.concat function can concatenate an arbitrary number of bytes or bytes1 ... bytes32 values.
The function returns a single bytes memory array that contains the contents of the arguments without padding.
If you want to use string parameters or other types that are not implicitly convertible to bytes, you need to convert them to bytes or bytes1/…/bytes32 first.

// SPDX-License-Identifier: GPL-3.0
pragma solidity ^0.8.12;

contract C {
    string s = "Storage";
    function f(bytes calldata bc, string memory sm, bytes16 b) public view {
        string memory concatString = string.concat(s, string(bc), "Literal", sm);
        assert((bytes(s).length + bc.length + 7 + bytes(sm).length) == bytes(concatString).length);

        bytes memory concatBytes = bytes.concat(bytes(s), bc, bc[:2], "Literal", bytes(sm), b);
        assert((bytes(s).length + bc.length + 2 + 7 + bytes(sm).length + b.length) == concatBytes.length);
    }
}

If you call string.concat or bytes.concat without arguments they return an empty array.

Memory arrays with dynamic length can be created using the new operator.
As opposed to storage arrays, it is not possible to resize memory arrays (e.g. the .push member functions are not available).
You either have to calculate the required size in advance or create a new memory array and copy every element.

As all variables in Solidity, the elements of newly allocated arrays are always initialized with the default value.

// SPDX-License-Identifier: GPL-3.0
pragma solidity >=0.4.16 <0.9.0;

contract C {
    function f(uint len) public pure {
        uint[] memory a = new uint[](7);
        bytes memory b = new bytes(len);
        assert(a.length == 7);
        assert(b.length == len);
        a[6] = 8;
    }
}

An array literal is a comma-separated list of one or more expressions, enclosed in square brackets ([...]).
For example [1, a, f(3)].
The type of the array literal is determined as follows:

It is always a statically-sized memory array whose length is the number of expressions.

The base type of the array is the type of the first expression on the list such that all other expressions can be implicitly converted to it. It is a type error if this is not possible.

It is not enough that there is a type all the elements can be converted to. One of the elements has to be of that type.

In the example below, the type of [1, 2, 3] is uint8[3] memory, because the type of each of these constants is uint8.
If you want the result to be a uint[3] memory type, you need to convert the first element to uint.

// SPDX-License-Identifier: GPL-3.0
pragma solidity >=0.4.16 <0.9.0;

contract C {
    function f() public pure {
        g([uint(1), 2, 3]);
    }
    function g(uint[3] memory) public pure {
        // ...
    }
}

The array literal [1, -1] is invalid because the type of the first expression is uint8 while the type of the second is int8 and they cannot be implicitly converted to each other.
To make it work, you can use [int8(1), -1], for example.

Since fixed-size memory arrays of different type cannot be converted into each other (even if the base types can), you always have to specify a common base type explicitly if you want to use two-dimensional array literals:

// SPDX-License-Identifier: GPL-3.0
pragma solidity >=0.4.16 <0.9.0;

contract C {
    function f() public pure returns (uint24[2][4] memory) {
        uint24[2][4] memory x = [[uint24(0x1), 1], [0xffffff, 2], [uint24(0xff), 3], [uint24(0xffff), 4]];
        // The following does not work, because some of the inner arrays are not of the right type.
        // uint[2][4] memory x = [[0x1, 1], [0xffffff, 2], [0xff, 3], [0xffff, 4]];
        return x;
    }
}

Fixed size memory arrays cannot be assigned to dynamically-sized memory arrays, i.e. the following is not possible:

// SPDX-License-Identifier: GPL-3.0
pragma solidity >=0.4.0 <0.9.0;

// This will not compile.
contract C {
    function f() public {
        // The next line creates a type error because uint[3] memory
        // cannot be converted to uint[] memory.
        uint[] memory x = [uint(1), 3, 4];
    }
}

It is planned to remove this restriction in the future, but it creates some complications because of how arrays are passed in the ABI.

If you want to initialize dynamically-sized arrays, you have to assign the individual elements:

// SPDX-License-Identifier: GPL-3.0
pragma solidity >=0.4.16 <0.9.0;

contract C {
    function f() public pure {
        uint[] memory x = new uint[](3);
        x[0] = 1;
        x[1] = 3;
        x[2] = 4;
    }
}

• length:
  Arrays have a length member that contains their number of elements.
  The length of memory arrays is fixed (but dynamic, i.e. it can depend on runtime parameters) once they are created.

• push():
  Dynamic storage arrays and bytes (not string) have a member function called push() that you can use to append a zero-initialised element at the end of the array.
  It returns a reference to the element, so that it can be used like x.push().t = 2 or x.push() = b.

• push(x):
  Dynamic storage arrays and bytes (not string) have a member function called push(x) that you can use to append a given element at the end of the array.
  The function returns nothing.

• pop():
  Dynamic storage arrays and bytes (not string) have a member function called pop() that you can use to remove an element from the end of the array.
  This also implicitly calls delete on the removed element.
  The function returns nothing.

// SPDX-License-Identifier: GPL-3.0
pragma solidity >=0.6.0 <0.9.0;

contract ArrayContract {
    uint[2**20] aLotOfIntegers;
    // Note that the following is not a pair of dynamic arrays but a
    // dynamic array of pairs (i.e. of fixed size arrays of length two).
    // In Solidity, T[k] and T[] are always arrays with elements of type T,
    // even if T itself is an array.
    // Because of that, bool[2][] is a dynamic array of elements
    // that are bool[2]. This is different from other languages, like C.
    // Data location for all state variables is storage.
    bool[2][] pairsOfFlags;

    // newPairs is stored in memory - the only possibility
    // for public contract function arguments
    function setAllFlagPairs(bool[2][] memory newPairs) public {
        // assignment to a storage array performs a copy of ``newPairs`` and
        // replaces the complete array ``pairsOfFlags``.
        pairsOfFlags = newPairs;
    }

    struct StructType {
        uint[] contents;
        uint moreInfo;
    }
    StructType s;

    function f(uint[] memory c) public {
        // stores a reference to ``s`` in ``g``
        StructType storage g = s;
        // also changes ``s.moreInfo``.
        g.moreInfo = 2;
        // assigns a copy because ``g.contents``
        // is not a local variable, but a member of
        // a local variable.
        g.contents = c;
    }

    function setFlagPair(uint index, bool flagA, bool flagB) public {
        // access to a non-existing index will throw an exception
        pairsOfFlags[index][0] = flagA;
        pairsOfFlags[index][1] = flagB;
    }

    function changeFlagArraySize(uint newSize) public {
        // using push and pop is the only way to change the
        // length of an array
        if (newSize < pairsOfFlags.length) {
            while (pairsOfFlags.length > newSize)
                pairsOfFlags.pop();
        } else if (newSize > pairsOfFlags.length) {
            while (pairsOfFlags.length < newSize)
                pairsOfFlags.push();
        }
    }

    function clear() public {
        // these clear the arrays completely
        delete pairsOfFlags;
        delete aLotOfIntegers;
        // identical effect here
        pairsOfFlags = new bool[2][](0);
    }

    bytes byteData;

    function byteArrays(bytes memory data) public {
        // byte arrays ("bytes") are different as they are stored without padding,
        // but can be treated identical to "uint8[]"
        byteData = data;
        for (uint i = 0; i < 7; i++)
            byteData.push();
        byteData[3] = 0x08;
        delete byteData[2];
    }

    function addFlag(bool[2] memory flag) public returns (uint) {
        pairsOfFlags.push(flag);
        return pairsOfFlags.length;
    }

    function createMemoryArray(uint size) public pure returns (bytes memory) {
        // Dynamic memory arrays are created using `new`:
        uint[2][] memory arrayOfPairs = new uint[2][](size);

        // Inline arrays are always statically-sized and if you only
        // use literals, you have to provide at least one type.
        arrayOfPairs[0] = [uint(1), 2];

        // Create a dynamic byte array:
        bytes memory b = new bytes(200);
        for (uint i = 0; i < b.length; i++)
            b[i] = bytes1(uint8(i));
        return b;
    }
}

When working with storage arrays, you need to take care to avoid dangling references.
A dangling reference is a reference that points to something that no longer exists or has been moved without updating the reference.
A dangling reference can for example occur, if you store a reference to an array element in a local variable and then .pop() from the containing array:

// SPDX-License-Identifier: GPL-3.0
pragma solidity >=0.8.0 <0.9.0;

contract C {
    uint[][] s;

    function f() public {
        // Stores a pointer to the last array element of s.
        uint[] storage ptr = s[s.length - 1];
        // Removes the last array element of s.
        s.pop();
        // Writes to the array element that is no longer within the array.
        ptr.push(0x42);
        // Adding a new element to ``s`` now will not add an empty array, but
        // will result in an array of length 1 with ``0x42`` as element.
        s.push();
        assert(s[s.length - 1][0] == 0x42);
    }
}

The write in ptr.push(0x42) will not revert, despite the fact that ptr no longer refers to a valid element of s.
Since the compiler assumes that unused storage is always zeroed, a subsequent s.push() will not explicitly write zeroes to storage, so the last element of s after that push() will have length 1 and contain 0x42 as its first element.

Note that Solidity does not allow to declare references to value types in storage.
These kinds of explicit dangling references are restricted to nested reference types.
However, dangling references can also occur temporarily when using complex expressions in tuple assignments:

// SPDX-License-Identifier: GPL-3.0
pragma solidity >=0.8.0 <0.9.0;

contract C {
    uint[] s;
    uint[] t;
    constructor() {
        // Push some initial values to the storage arrays.
        s.push(0x07);
        t.push(0x03);
    }

    function g() internal returns (uint[] storage) {
        s.pop();
        return t;
    }

    function f() public returns (uint[] memory) {
        // The following will first evaluate ``s.push()`` to a reference to a new element
        // at index 1. Afterwards, the call to ``g`` pops this new element, resulting in
        // the left-most tuple element to become a dangling reference. The assignment still
        // takes place and will write outside the data area of ``s``.
        (s.push(), g()[0]) = (0x42, 0x17);
        // A subsequent push to ``s`` will reveal the value written by the previous
        // statement, i.e. the last element of ``s`` at the end of this function will have
        // the value ``0x42``.
        s.push();
        return s;
    }
}

It is always safer to only assign to storage once per statement and to avoid complex expressions on the left-hand-side of an assignment.

You need to take particular care when dealing with references to elements of bytes arrays, since a .push() on a bytes array may switch from short to long layout in storage.

// SPDX-License-Identifier: GPL-3.0
pragma solidity >=0.8.0 <0.9.0;

// This will report a warning
contract C {
    bytes x = "012345678901234567890123456789";

    function test() external returns(uint) {
        (x.push(), x.push()) = (0x01, 0x02);
        return x.length;
    }
}

Here, when the first x.push() is evaluated, x is still stored in short layout, thereby x.push() returns a reference to an element in the first storage slot of x.
However, the second x.push() switches the bytes array to large layout.
Now the element that x.push() referred to is in the data area of the array while the reference still points at its original location, which is now a part of the length field and the assignment will effectively garble the length of x.
To be safe, only enlarge bytes arrays by at most one element during a single assignment and do not simultaneously index-access the array in the same statement.

While the above describes the behaviour of dangling storage references in the current version of the compiler, any code with dangling references should be considered to have undefined behaviour.
In particular, this means that any future version of the compiler may change the behaviour of code that involves dangling references.

Be sure to avoid dangling references in your code!

Array slices are a view on a contiguous portion of an array.
They are written as x[start:end], where start and end are expressions resulting in a uint256 type (or implicitly convertible to it).
The first element of the slice is x[start] and the last element is x[end - 1].

If start is greater than end or if end is greater than the length of the array, an exception is thrown.

Both start and end are optional: start defaults to 0 and end defaults to the length of the array.

Array slices do not have any members.
They are implicitly convertible to arrays of their underlying type and support index access.
Index access is not absolute in the underlying array, but relative to the start of the slice.

Array slices do not have a type name which means no variable can have an array slices as type, they only exist in intermediate expressions.

Array slices are useful to ABI-decode secondary data passed in function parameters:

// SPDX-License-Identifier: GPL-3.0
pragma solidity >=0.8.5 <0.9.0;
contract Proxy {
    /// @dev Address of the client contract managed by proxy i.e., this contract
    address client;

    constructor(address client_) {
        client = client_;
    }

    /// Forward call to "setOwner(address)" that is implemented by client
    /// after doing basic validation on the address argument.
    function forward(bytes calldata payload) external {
        bytes4 sig = bytes4(payload[:4]);
        // Due to truncating behaviour, bytes4(payload) performs identically.
        // bytes4 sig = bytes4(payload);
        if (sig == bytes4(keccak256("setOwner(address)"))) {
            address owner = abi.decode(payload[4:], (address));
            require(owner != address(0), "Address of owner cannot be zero.");
        }
        (bool status,) = client.delegatecall(payload);
        require(status, "Forwarded call failed.");
    }
}

Solidity provides a way to define new types in the form of structs, which is shown in the following example:

// SPDX-License-Identifier: GPL-3.0
pragma solidity >=0.6.0 <0.9.0;

// Defines a new type with two fields.
// Declaring a struct outside of a contract allows
// it to be shared by multiple contracts.
// Here, this is not really needed.
struct Funder {
    address addr;
    uint amount;
}

contract CrowdFunding {
    // Structs can also be defined inside contracts, which makes them
    // visible only there and in derived contracts.
    struct Campaign {
        address payable beneficiary;
        uint fundingGoal;
        uint numFunders;
        uint amount;
        mapping (uint => Funder) funders;
    }

    uint numCampaigns;
    mapping (uint => Campaign) campaigns;

    function newCampaign(address payable beneficiary, uint goal) public returns (uint campaignID) {
        campaignID = numCampaigns++; // campaignID is return variable
        // We cannot use "campaigns[campaignID] = Campaign(beneficiary, goal, 0, 0)"
        // because the right hand side creates a memory-struct "Campaign" that contains a mapping.
        Campaign storage c = campaigns[campaignID];
        c.beneficiary = beneficiary;
        c.fundingGoal = goal;
    }

    function contribute(uint campaignID) public payable {
        Campaign storage c = campaigns[campaignID];
        // Creates a new temporary memory struct, initialised with the given values
        // and copies it over to storage.
        // Note that you can also use Funder(msg.sender, msg.value) to initialise.
        c.funders[c.numFunders++] = Funder({addr: msg.sender, amount: msg.value});
        c.amount += msg.value;
    }

    function checkGoalReached(uint campaignID) public returns (bool reached) {
        Campaign storage c = campaigns[campaignID];
        if (c.amount < c.fundingGoal)
            return false;
        uint amount = c.amount;
        c.amount = 0;
        c.beneficiary.transfer(amount);
        return true;
    }
}

The contract does not provide the full functionality of a crowdfunding contract, but it contains the basic concepts necessary to understand structs.
Struct types can be used inside mappings and arrays and they can themselves contain mappings and arrays.

It is not possible for a struct to contain a member of its own type, although the struct itself can be the value type of a mapping member or it can contain a dynamically-sized array of its type.
This restriction is necessary, as the size of the struct has to be finite.

Note how in all the functions, a struct type is assigned to a local variable with data location storage.
This does not copy the struct but only stores a reference so that assignments to members of the local variable actually write to the state.

Of course, you can also directly access the members of the struct without assigning it to a local variable, as in campaigns[campaignID].amount = 0.