The book is devoted to the theory of induced representations of groups and its applications in particle physics. The first part contains a description of the theory of induced representations of groups calculated by physicists and methods of constructing irreducible representations of non-compact groups based on it. As examples important for applications, unitary irreducible representations of the Poincaré, Lorentz and de Sitter groups are built. The second part of the book reveals the role of induced representations in the description of quantum systems with symmetry groups. On this basis, the theory of interacting particles in space-time is built with the geometric structure of one of the following three types: Galilean space, Minkowski space and de Sitter space (space of constant curvature). These models are analyzed from a single point of view, which can be formulated as a principle of quantization that does not contain the concept of a quantized field.