Collection of problems in the theory of analytical functions" is intended for students of universities, pedagogical institutes and higher educational institutions studying the theory of functions of a complex variable. It is designed in such a way that it is convenient to use it in any construction of a lecture course. To this end, individual paragraphs are written mainly independently of each other and are divided into task cycles united by a common idea. Problems of increased difficulty are usually placed at the end of cycles. All basic facts and definitions are given where they are used.