Locally semisimple algebras. Combinatorial theory and the K0-functor

Survey is devoted to theory of locally finite algebras and approximately finite-dimensional ¦AF-¦C^*-algebras which has been developed intensively in recent years. It can serve as an introduction to the subject. Both known and new results are contained in it.Translated from Itogi Nauki i Tekhniki, Sovremennye Problemy Matematiki, Noveishie Dostizheniya, Vol. 26, pp. 3–56, 1985.