In the 1930s, Reidemeister first rigorously proved that knots exist which are distinct from the unknot. He did this
by showing that all knot deformations can be reduced to
a sequence of three types of "moves," called the (I) twist
move, (II) poke move, and (III) slide
move. These moves are most commonly called Reidemeister moves, although the term
"equivalence moves" is sometimes also used (Aneziris 1999, p. 29).

Aneziris, C. N. "The Equivalence Moves." Ch. 4 in The
Mystery of Knots: Computer Programming for Knot Tabulation. Singapore: World
Scientific, pp. 29-33, 1999.Hoste, J.; Thistlethwaite, M.; and
Weeks, J. "The First Knots." Math. Intell.20, 33-48,
Fall 1998.Kauffman, L. Knots
and Physics. Teaneck, NJ: World Scientific, p. 16, 1991.Reidemeister,
K. "Knotten und Gruppen." Abh. Math. Sem. Univ. Hamburg5,
7-23, 1927.