The work is the third volume of a four-volume textbook on mathematics that covers the material for the mathematical preliminary examination. It is aimed at students of mathematics, computer science, physics, and geophysics and addresses analysis in several variables. The focus is on differential calculus in finite-dimensional spaces and Lebesgue integral calculus based on measure theory. Additionally, it provides an introduction to topology, complex analysis, and stochastic processes. Numerous examples, particularly from physics, and extensive exercise material complement the presentation.