The book "Initial chapters of mathematical analysis in a semi-formal presentation" is a unique work created by a team of authors that opens the door to the world of mathematical analysis for students, teachers and anyone who seeks to deepen their knowledge in this important area of mathematics. This edition will become an indispensable assistant for those who want not only to master the basics of analysis, but also to understand its philosophical and practical aspects. From the first pages, the reader plunges into the fascinating world of mathematical concepts, where each definition and theorem is substantiated and illustrated by clear examples. The authors seek to create a semi-formal presentation, which avoids excessive abstraction, often found in traditional textbooks. Instead, they invite the reader to become aware of and feel how the basic ideas of mathematical analysis work, from limits and continuity to derivatives and integrals. This makes the book available to a wide audience, including high school students, university students, and even people who are simply interested in mathematics. Who can like this edition? First of all, students studying mathematics, physics, engineering and other technical disciplines . The book will be useful for those who are preparing for exams, as well as for those who want to refresh their knowledge and prepare for more complex topics. It will also attract the attention of teachers who are looking for quality and affordable materials for their students. Finally, lovers of mathematics who want to understand the basics of analysis will find in this book many interesting and useful ideas. The topics raised in the book cover a wide range of issues, ranging from the basics of mathematical analysis to its application in various fields of science and technology. The authors emphasize the importance of understanding the limits, continuity of functions and their derivatives, which is the basis for further study of more complex topics, such as multidimensional analysis and functional analysis. The book also touches on the philosophical aspects of mathematics, emphasizing that analysis is not just a set of formulas, but a whole science of the laws and structure that surround us in the real world. The style of the authors is clear and accessible, which makes reading easy and exciting. They use many examples and problems that help the reader to consolidate the material studied and see the practical application of mathematical concepts. This makes the book not only a textbook, but also a real guide to the world of mathematical analysis. If you are looking for something similar, pay attention to other famous works in the field of mathematical analysis, such as “Mathematical Analysis” by Tikhomirov or “