The work is aimed at the systematic study of a wide field of problems related to closely related areas of modern general algebra, namely, the theory of semigroups (including related types of algebras such as epigroups and monoids), the theory of associative rings and algebras, and the theory of lattices. The main attention is paid to the problems related to the theory of varieties (questions of the finite basis property, the structure of algebras in varieties, the lattices of subvarieties) and the structural theory of algebras of the types listed.