This book is dedicated to the memory of S. Ya. Khavinson. The introductory note is written by V. P. Havin. It recalls the main results of S. Ya. Khavinson, in particular results in linear programming and complex analysis (Khavinson’s approach to extremal problems), extremal problems with supplementary restrictions (a Tchebyshev-like phenomenon), spaces of analytic functions in multiply connected domains (zero logarithmic capacity of removable sets and factorization problems), analytic capacity (Khavinson’s measure and Cauchy potentials) and approximation problems. A complete bibliography and several photos are included. Moreover, the book contains twelve research and expository papers covering the following topics: extremal problems, approximation problems, the Cauchy integral, analytic capacity, Cantor sets, meromorphic functions, the Carathéodory inequality, and the integral representation of functions and the shift operator. The book is suitable for graduate students and researchers in analysis.