The term "quanturn groups" was popularized by Drinfeld in his address to the International Congress of Mathematicians in Berkeley(1986). It stands for certain special Hopf algebras which are nontrivial deformations of the enveloping Hopf algebras of semisimple Lie algebras or of the algebras of regular functions on the corresponding algebraic groups. As was soon observed, quantum groups have close connections with varied, a priori remote, areas of mathematics and physics.本書為英文版。