Knight's Tours have fascinated mathematicians for centuries. A Knight's Tour is a set of moves made by the knight on a chessboard, on which the piece visits each square exactly one time. Leonhard Euler was the first to write a mathematical paper analyzing these tours.
If you are unfamiliar with chess, the knight piece may move in an "L" shape; it can move two squares horizontally and one square vertically, or two squares vertically and one square horizontally.
A tour is called closed or reentrant if the knight ends its tour on a square that is one move away from the square it started (meaning it could begin the same tour over again). Otherwise it is an open tour.
Apart from the standard 8x8 square chessboard, Knight's Tours have been studied on boards with varying dimensions as well as on irregular (not square) surfaces.
Below is an animation of an open Knight's Tour on a 5x5 chessboard.