Some of the most famous questions in mathematical history have involved equations with coefficients in Z, the set of integers. This book deals with their solutions, which are achieved with an economy of effort through the process of abstraction. It presents both results and their underlying ideas, thus introducing the basic concepts of groups, rings and fields to solve long-standing problems in mathematics. Among the subjects covered are results from number theory, the fundamental theory of algebra, the unconstructability of certain numbers, the characterization of all infinite fields and the unsolvability of the general equation of degree 5.
