The book is devoted to the presentation of matrix theory and its applications to the theory of differential equations, mathematical economics, and probability theory. The monograph is written in such a way that it can also be read by a student who has not previously studied linear algebra. There are 600 tasks in the book; many of them lead the reader to independent scientific activity in the field of matrix theory. The value of the book is increased by the reviews of the latest original works in the corresponding field given at the end of each chapter.