This manual covers the mathematical methods necessary for students of mathematics, physics, and engineering. The purpose of the book is to present theoretical concepts in a simple and understandable way and show the possibility of applying them to practical problems in the natural sciences and engineering. The work covers the following: Linear algebra and matrix theory; Differential equations and their physical applications; Special functions and solving physical problems with their help; Fourier and Laplace transforms; Complex analysis methods; Integral equations and variational methods; Practical application of probability and statistical methods. The book is enriched not only with theoretical foundations, but also with numerous examples, exercises, and applications, preparing the reader for scientific research and solving practical problems.