ABSTRACT
The main content of modern algebra (abstract algebra) is the alge-braic system-a nonempty set-together with one or more binary operations (also called algebraic operations) defined on it. This book will mainly cover three basic algebraic systems-groups, rings, and fields. In this chapter, we introduce some basic concepts that are closely related to these three basic algebraic systems. The concepts include maps between sets, binary operations, homomorphisms and isomorphisms between sets equipped with binary operations, and equivalence relations.
