The book, containing four chapters, is devoted congruences of some types in semigroups (we study certain congruences on very wide classes of semi- groups such that the quotient semigroups belong to most important classes of semigroups). In this book are described matrix congruences, group congruences, rectangular group congruences, Clifford congruences, E-unitary congruences, UBG-congruences, OBG-congruences, etc. on certain semigroups with very big classes of semigroups (e.g. E-inversive semigroups, eventually regular semigroups, structurally regular semigroups, idempotent-surjective semigroups).