In this book the problems of approximability of functions by polyanalytic polynomials in the spaces of continuous and smooth functions on compact subset of the complex plane are considered. The book includes classical results in the themes under consideration as well as recent result of the author and his colleagues and collaborators. The book is intended to researchers working in complex analysis and approximation theory. In may be used as the material for special courses on theory of approximations by analytic functions for undergraduate and postgraduate students in mathematics.
