Kurt Reidemeister was able to prove that any ambient isotopy with knots and links can be expressed in the terms of only three types of moves. These became known as the Reidemeister Moves.
Below is an image showing the three Reidemeister Moves. A type I move adds or removes a trivial crossing. A type II move adds or removes a trivial arc and two crossings. A type III move allows an arc to be moved to the other side of a crossing.