  In 1992 V.Drinfeld formulated a number of problems in quantum group theory.
In particular, he suggested to consider ``set-theoretical'' solutions to the
quantum Yang-Baxter equation, i.e. solutions given by a permutation R of the
set $X\times X$, where X is a fixed set. In this paper we study such solutions,
which in addition satisfy the unitarity and nondegeneracy conditions. We
discuss the geometric and algebraic interpretations of such solutions,
introduce several constructions of them, and make first steps towards their
classification.
