The book is devoted to the thorough study of polyadic (higher arity) algebraic structures which has a long history starting from 19th century. The main idea was to take a single set closed under one binary operation and to generalize it by increasing the arity of the operation called a polyadic operation. Until now a general approach to polyadic concrete many-set algebraic structures was absent. We propose to investigate algebraic structures in the concrete way and provide consequent polyadization of each operation starting from group-like structures and finishing with the Hopf algebra structures. Polyadic analogs of homomorphisms which change arity heteromorphisms are introduced and applied for constructing unusual representations multiactions matrix representations and polyadic analogs of direct product. We provide the polyadic generalization of the Yang-Baxter equation find its constant solutions and introduce polyadic tensor categories. Suitable for university students of advanced level algebra courses and mathematical physics courses. Key Features: Provides a general unified approachWidens readers perspective of the possibilities to develop standard algebraic structuresProvides the new kind of homomorphisms changing the arity heteromorphisms are introduced and applied for construction of new representations multiactions and matrix representationsPresents applications of polyadization approach to concrete algebraic structures. Language: English