A presentation of the classic procedures of polynomial algebra that are computationally relevant. The first chapter discusses the construction and representation of polynomials, while the second focuses on the computational aspects of their analytical theory. Polynomials with coefficients in a finite field are then described in chapter three and the final chapter is devoted to factorization with integral coefficients. Aimed primarily at graduates with a prerequisite knowledge of set theory, usual fields and basic algebra, the text contains fully worked-out examples, hints and references, and details concerning the implementation of algorithms as well as indicators of their efficiency.