The textbook covers, in particular, the following questions: partially ordered sets and axiom of choice, groups, semigroups and inverse semigroups, quasigroups and magnifiers, rings, semigrouds, associative and non-associative rings, universal algebras, groups with multioperators, structures, modules, linear algebras, ordered and topological groups and rings, normalized and differential rings. Like other well-known textbooks by A. G. Kurosh ("Course of Higher Algebra," "Theory of Groups"), the book is distinguished by the clarity of the presentation of the material.