Congruences of finite multibase universal algebras

The subset of congruences of a finite multibasic universal algebra (called the set of maximal conguences) which determines the whole set of congruences is found. The optimality of some method of equation solving with the use of maximal congruences is demonstrated; congruences of quasigroups which are isotopic and cross-isotopic to groups are described. The existence of simple (having no non-trivial congruences) universal algebras defined on sets of any finite orders is proved. With the use of wreath product construction, extensions of multibasic universal algebras are described.