This book aims to assist first-year students in the departments of natural sciences to understand the various concepts of the mathematical unit "Sequences of real numbers." This is achieved through a comprehensible yet concise presentation of the relevant theory, with numerous examples and a large number of solved exercises.

The book consists of five chapters:

The first chapter contains the necessary introductory concepts. (Basic inequalities - sums - integer part of a real number - the set IR and its subsets - Elements from the topology of IR.)

The second chapter contains the introductory concepts of sequences (presentation of a sequence, monotonicity, boundedness, graphical representation).

The third chapter deals with the convergence and the limit convergence of sequences. Special emphasis is placed on the "epsilon" definition of convergence as well as on "trivial" limits.

The fourth chapter contains various extended concepts of sequences. (Sequences of closed intervals, accumulation points of a sequence, basic sequences, convergent sequences, and upper-lower bounds of a sequence.)

The fifth chapter refers to the applications of function theory to sequences. All chapters are accompanied by examples, solved exercises, and the necessary methodology.

After the fifth chapter, there is a series of simple solved exercises covering the entire spectrum of the theory. After these exercises, General Exercises - topics from various Greek and foreign universities are included. We believe that this book will receive the same reception as the other books in the series "Aithra - Library of Higher Mathematics."

Contains: - Concise theory, - Methodology, - 400 solved exercises.