This subject is an introduction to abstract algebra in which we study the main properties of groups, rings and fields. Each one of these objects is an algebraic structure: a mathematical object that is defined as a set with some operations on it that satisfy certain axioms. This axiomatic description allows to explore general and abstract properties of these algebraic structures that can be applied to particular examples. In this subject, we will also study applications of abstract algebra to engineering, physics, and other branches of mathematics.