"The Theory of Anisotropic Elastic Plates" is a technical book that deals with the mathematical theory of elastic plates and shells. It aims to investigate fundamental boundary value problems of spatial elasticity theory in cylindrical domains and to reduce these to two-dimensional boundary value problems. The work provides a comprehensive analysis of reduction methods known in the literature as simplifying hypotheses. Unlike classical approaches, it addresses refined theories of anisotropic, non-homogeneous plates with variable thickness without physical and geometric constraints. The study also includes the solvability and convergence of processes, as well as the development of effective algorithms for approximate solutions. This book is a valuable resource for professionals and students who wish to engage with advanced concepts of elasticity theory.