These notes were written to serve as a aid for students of Higher Education Institutions, but also for anyone who wants to understand and study the Sequences of real numbers.

In the first chapter, we introduce the basic characteristics and properties of sets: bounded sets, limit points of sets, upper bounds, lower bounds, etc. We also present the inequality relations and other relations that are useful for the continuation.

In the following chapters, we provide the definition of a sequence, its characteristics, and properties: Monotonicity, boundedness, limit - convergence. Then we deal with finding the formula of a sequence from a recursive relation. Next, we introduce the upper and lower limits. Finally, we present the method for calculating the limit of a sequence using the derivative of a function.

In all the above, every possible effort has been made for simplification, making it easier to understand. The observations of the reader are always welcome.

[Excerpt from the introductory text]