Mathematical Analysis of the Limit and Continuity of Function : Methodological guidelines for the study of discipline and implementation”, prepared by the team of authors, is an indispensable educational resource for students, teachers and anyone who seeks to better understand the fundamental aspects of mathematical analysis. This work is not just a manual, but a real guide to one of the most important sections of mathematics, revealing the intricacies and nuances of the topic “The Limit and Continuity of a Function” with clarity and accessibility, which makes it especially attractive to a wide range of readers. The book focuses on the concepts of limit and continuity, which underlie analysis and serve as the basis for further research and solutions of complex mathematical problems. The authors masterfully analyze the theoretical foundations, giving examples illustrating key ideas, and pay special attention to practical aspects - the execution of tasks, preparation for exams and independent mastering of the material. The book discusses in detail the various methods of defining limits, the properties of continuous functions, as well as their importance in the construction of mathematical models, which makes it a valuable tool for consolidating knowledge and developing analytical thinking. This textbook is perfect for students studying mathematical analysis in the first courses of universities, as well as teachers looking for structured and understandable material for classes. It is designed for an audience from beginners to those who already have basic knowledge and want to deepen their skills. The book will be of interest to those who appreciate a systematic approach, a clear structure of the presentation of material and practical orientation, because there are many exercises, tasks and methodological recommendations that allow to consolidate the theory in practice. The peculiarity of this publication is its focus on the development of logical thinking and analytical skills .. The authors use a modern style of presentation, avoiding complex terms without explanation, which makes the book understandable even for those who are just beginning to get acquainted with mathematical analysis. At the same time, the material is presented in sufficient depth and detail, which allows the reader to get a full understanding of the limit and continuity, as well as to understand their role in more complex sections of mathematics. The book "Mathematical analysis under the section "Limit and continuity of function": Methodical guidelines for the study of discipline and performance" deserves attention not only as a textbook, but also as a source of inspiration for independent research and in-depth study. It raises important topics such as the properties of limits, criteria for their existence, theorems on continuous functions, and methods for proving them, making it a worthy part of any student or teacher library. If you are looking for a book that will not only help you understand the theory, but also teach you how to apply knowledge in practice, master complex concepts and prepare for exams, then this publication will be a reliable assistant for you. It combines a rigorous scientific style with accessibility, which makes the material understandable and interesting. Get inspired, explore and expand your mathematical horizons along with this unique tutorial created by a team of professionals for those who appreciate the quality and depth of knowledge This book is an excellent choice for those who want not only to memorize definitions and formulas, but also to learn how to think mathematically, see connections and patterns, and prepare for further development in the field of analysis. Do not miss the chance to make your path in mathematics fascinating and effective with this detailed and methodically verified guide.