It is known that by the term "Algebra" in Higher Mathematics we now mean "Abstract Algebra" which has as its object Algebraic Structures (link theory, groups, fields, rings, categories, homological algebra, universal algebra).
The purpose of this book is to help the students of the mathematics departments of the country's universities on the one hand to understand the basic concepts of the course "Algebra" (or "Algebra I") (integers, groups, rings, fields, modules) and on the other hand to acquire the required experience in solving the exercises. The book is divided into three chapters which respectively contain the concepts "Sets-Relations-Integers, Groups and Rings". Each chapter contains brief theory and some categories of solved exercises.
It was considered appropriate for the sake of completeness to include additional topics that are not taught in some mathematics departments, such as group action, modules (patterns), Noether rings, extensions of bodies, etc.
The exercises in each category cover a wide range of concepts related to the respective heading. A part of these exercises have been prepared by the author of the book, while several exercises have been selected from the Greek and foreign language literature. They even contain exercises that have been given as subjects in undergraduate and qualifying exams of mathematics departments of Greek and foreign universities.