Quantum groups

The article is an extended version of the author's report presented to the International Congress of Mathematicians in Berkeley, 1986. It contains a survey of the new algebraic formalism based on the notion of Hopf algebras and designed to serve an algebraic foundation of the Quantum Inverse Scattering Method, numerous examples of Hopf algebras which are both non-commutative and non-commutative are delivered and their connection with the solutions of the Quantum Yang–Baxter Identity is explained.