  Cycle sets are algebraic structures introduced by Rump to study set theoretic
solutions to the Yang-Baxter equation. While studying cycle sets Rump also
introduced braces, which have since overtaken cycle sets as a tool for studying
solutions. This survey paper is primarily an introduction to cycle sets,
motivating their study and relating them to key results of brace theory and
Yang-Baxter theory. It is aimed at anyone from those already very familiar with
braces but less familiar with cycle sets, to those with only a basic level of
background in ring theory and group theory. We introduce cycle sets following
Rump's original results - giving more detailed, easy to follow versions of his
proofs - and then relate them back to left braces. We also go on to discuss
interesting constructions of cycle sets which do not necessarily correspond
directly to braces.
