This is the English translation of Kaljulaid's 1979 Tartu/Minsk Candidate thesis, which originally was typewritten in Russian and manufactured in not so many copies. The thesis was devoted to representation theory in the spirit of his thesis advisor B. I. Plotkin: representations of semigroups and algebras, especially extension to this situation, and application of the notion of triangular product of representations for groups introduced by Plotkin. Through representation theory, Kaljulaid became also interested in automata theory, which at a later phase became his main area of interest. Another field of research concerns combinatorics. Besides being an outstanding and most dedicated mathematician Uno Kaljulaid was also very much interested in the history of mathematics. Kaljulaid was also very interested in the teaching and exposition, or popularization of mathematics. There is a whole series of papers about algebraic matters, culminating in a brilliant, elementary - although partly rather philosophical - essay devoted to Galois theory. Another such series is his excellent essay of Diophantine Geometry in various installments, followed by his eloge to another of his teachers Yu. I. Manin. We believe that the inclusion of these papers here will make it more interesting for beginners, and perhaps even contribute to attracting young people to mathematics.IOS Press is an international science, technical and medical publisher of high-quality books for academics, scientists, and professionals in all fields. Some of the areas we publish in: -Biomedicine -Oncology -Artificial intelligence -Databases and information systems -Maritime engineering -Nanotechnology -Geoengineering -All aspects of physics -E-governance -E-commerce -The knowledge economy -Urban studies -Arms control -Understanding and responding to terrorism -Medical informatics -Computer Sciences