A real contribution to mathematical analysis, a discipline that requires a great deal of study and attention and finds interesting applications in many disciplines of sciences and engineering.This book is designed for graduate students in mathematics and engineering. From the first chapters, the book introduces real and complex numbers, the cornerstones of analysis. It explains in detail the properties of real numbers, such as the square root, absolute value. The analysis of sequences and series occupies a central place in this textbook. The reader discovers, step by step, the convergence through the study of real sequences, drawing on the concepts of Cauchy sequences and monotone sequences. The book also covers numerical series, presenting a variety of convergence criteria. The field of functions and asymptotic study of functions is treated with particular attention.The book contains proofs, numerous examples, and exercises with hints and solutions. The approach differs from similar books in that it is sequential, simplified concepts, and includes numerous solved examples and exercises that serve the reader, enabling them to understand the content well.