This monograph summarizes the author’s contributions to the study of algebras having their origin in logic. The book is divided into five chapters. The first four chapters (sets and functions, ordered sets, topics in universal algebra and topics in theory of categories) contain basic material, which is needed for the main part (algebras of logic). The corresponding chapter deals with several categories of algebras coming from intuitionistic logic, logic without contraction and fuzzy logic, in particular with Heyting algebras, Hilbert algebras, Hertz algebras, residuated lattices and Wajsberg algebras. The author concentrates on the algebraic and categorical properties of these structures contained in his numerous research articles. Historical background and motivation for the results described are not included; the reader is referred to the literature.