This book is a textbook for part-time students of pedagogical institutes. It is written in accordance with the current program and is devoted to the algebra of polynomials, which constitutes the last (fourth) part of the course "Algebra and Number Theory." The basic concepts of ring theory and the theory of divisibility in Euclidean rings are assumed to be known. On these issues, we refer the reader to the book "Algebra and Number Theory," part III, authors N. A. Kazachek, G. N. Perlatov, N. Ya. Vilenkin, A. li. Borodina (M, Enlightenment, 1974). Almost all sections of the algebra of polynomials are somehow related to the solution of algebraic equations and systems of equations. This material is especially close to the school mathematics course. Therefore, in this manual, a lot of attention is paid to the problem of solving equations, despite the fact that in modern polynomial algebra it occupies a modest place.