The monograph can be used for different tasks - from student special courses to a basis for further research. It presents a significant part of the author's papers. The results were reported at scientific conferences and congresses. Their formal or semantic connection is indicated. They are united by a study of prototypes at structure and automaton homomorphisms. The most original of the methods for that are grouped into an initial section with indications of their distribution to the separate chapters and sections. This approach allows a philosophy of science and mathematical motivation, substantiation, and advanced indication of the advisability of the received results. They unite different mathematical subjects from Logic, Algebra, and Theoretical Computer Science. This task is difficult, motivated and requires original approaches. One of them is the realized connection between solving algorithmic problems in Theory of Semigroups and Theory of Languages on the basis of a study of language prototypes. Prototypes of concepts with an important role in Computer science are also studied.