The book is a textbook on the theory of special functions, reflecting the significant progress in this area achieved in the second half of the 20th century. A significant part of the material presented cannot be found in standard monographs and reference books. The main subject of the book is one-dimensional hypergeometric functions in the broad sense of the word (including the functions of Gauss, Kummer, Bessel, senior pFq, as well as q-series). The G-function, various aspects of the theory of orthogonal polynomials (including neoclassical orthogonal systems of the Wilson type), multidimensional Selberg integrals, and analysis on the sphere are discussed in detail.