"Mathematical Analysis" . H. 1. Edited by E. N. Alekseeva is an outstanding textbook that has become a reference book for students, graduate students and anyone who seeks to better understand the basics of mathematical analysis. This paper is the first part of an extensive course covering key topics that form the foundation of mathematical thinking and analytical skills. The main goal of the book is to introduce the reader to the basics of mathematical analysis, starting with the limiting processes and ending with the elements of functional analysis. It discusses in detail important concepts such as the limits of sequences and functions, continuity, differentiation, and integration. Each section is written with clarity and logic, which allows the reader not only to learn the material, but also to see its practical application in various fields of science and technology. The book will be especially interesting for students of mathematical, physical, mathematical and engineering specialties, as well as for anyone who wants to deepen their knowledge in the field of analysis. It is suitable for both beginners and those who already have basic knowledge and want to systematize them. Teachers and researchers will also find it useful materials for preparing for lectures and seminars . The topics raised in the book go beyond the simple study of formulas and theorems. The author's team focuses on methods of solving problems, which helps the reader to develop critical thinking and analytical abilities. The book not only explains how to solve problems, but also helps to understand why these methods work. This makes it especially valuable for those who want not just to remember the material, but really realize it. The style in which the book is written differs in accessibility and logic. Each section begins with simple concepts and gradually deepens into more complex topics, which allows the reader to easily follow the course of thought of the authors. In addition, there are many examples and tasks in the book that help to consolidate the material studied .. This makes it not only a tutorial, but also a practical guide. E. N. Alexeyeva is known as the author and editor of many textbooks on mathematics, and his works are respected in the academic environment. Among his other well-known works can be distinguished "Mathematical analysis. H. 2. as well as various manuals on linear algebra and differential equations. Each of his books is distinguished by high quality of presentation and attention to detail, which makes them indispensable for students and teachers. "Mathematical Analysis" . H. 1. It is not just a textbook, but a real find for anyone who wants to master the art of mathematical analysis. It opens doors to the world of complex mathematical concepts, making them accessible and understandable. If you are looking for a quality tutorial that will help you not only learn, but also love mathematics, this publication will be an excellent choice. Do not miss the opportunity to immerse yourself in the fascinating world of analysis and develop your skills that will be useful to you in your studies and future career.