This collection is based on the material of classes on the course of mathematical analysis, studied in the third semester at the Faculty of Mechanics and Mathematics of Moscow State University ... It provides theoretical information and methodological instructions, as well as algorithms for solving entire classes of problems . This manual looks at numerical and functional series and has two sections: 'Series and infinite works', 'Applications of series theory'. Most of the tasks and exercises are different from those contained in the well-known task book B. P. Demidovich . For students and teachers of universities, pedagogical and technical universities .