Libraries are similar to contracts, but you can't declare any state variable and you can't send ether. A library is embedded into the contract if all library functions are internal. Otherwise the library must be deployed and then linked before the contract is deployed. // SPDX-License-Identifier: MIT pragma solidity ^0.8.13; library SafeMath { function add(uint x, uint y) internal pure returns (uint) { uint z = x + y; require(z >= x, "uint overflow"); return z; } } library Math { function sqrt(uint y) internal pure returns (uint z) { if (y > 3) { z = y; uint x = y / 2 + 1; while (x < z) { z = x; x = (y / x + x) / 2; } } else if (y != 0) { z = 1; } // else z = 0 (default value) } } contract TestSafeMath { using SafeMath for uint; uint public MAX_UINT = 2**256 - 1; function testAdd(uint x, uint y) public pure returns (uint) { return x.add(y); } function testSquareRoot(uint x) public pure returns (uint) { return Math.sqrt(x); } } // Array function to delete element at index and re-organize the array // so that their are no gaps between the elements. library Array { function remove(uint[] storage arr, uint index) public { // Move the last element into the place to delete require(arr.length > 0, "Can't remove from empty array"); arr[index] = arr[arr.length - 1]; arr.pop(); } } contract TestArray { using Array for uint[]; uint[] public arr; function testArrayRemove() public { for (uint i = 0; i < 3; i++) { arr.push(i); } arr.remove(1); assert(arr.length == 2); assert(arr[0] == 0); assert(arr[1] == 2); } }