Self-taught mass matrix system MATLAB, which occupies a leading place in the field of numerical scientific and technical calculations, calculations and modeling. The main focus is on the description of the basics of the application and programming language of the basic MATLAB system, the implementation of numerical calculation methods and the visual-oriented design of the graphical user interface (GUI). The features of the MATLAB interface, operators, functions and programming tools are described. Hundreds of examples of the use of MATLAB in educational, scientific, technical and mathematical calculations and calculations are given.