Textbook in PDF format The book provides exercises and problems with solutions in Galois Theory and its applications, which include finite fields, permutation polynomials, derivations and algebraic number theory. It will be useful to the audience below: Students who want to learn the material around the arithmetic of polynomials and field extensions. Teachers who want to work on problems with their students. Researchers who require a reference book. The book contains some useful results generally known by specialists, but for which a detailed proof is not always in the literature