The book "Analytical geometry and linear algebra" by Umnov A. E. is an exciting and deep dive into the world of mathematical science, which will be an indispensable tool for both students and teachers In this work, the author masterfully combines theory and practice, offering readers not only theoretical foundations, but also a variety of examples, tasks and exercises that will help consolidate the knowledge gained. The main goal of the book is to give the reader a clear understanding of the key concepts of analytical geometry and linear algebra. Umnov A. E. begins with the basics, gradually deepening into more complex topics, such as vectors, matrices, systems of linear equations and their geometric interpretation. Each chapter is imbued with logic and clarity, which makes the material accessible to those who do not have deep knowledge in mathematics. The book will be especially interesting for students of technical specialties, students of mathematical faculties and anyone who wants to deepen their knowledge in the field of mathematics. If you are preparing for exams, want to improve your skills in solving problems or just interested in mathematics, this publication will become your reliable companion. Umnov A. E. uses accessible language and understandable examples, which makes the learning process not only effective, but also fascinating. The topics raised in the book cover a wide range of issues, ranging from the basics of analytic geometry to more complex concepts such as eigenvalues and eigenvectors. Umnov focuses on the practical application of the theory, which allows the reader to see how mathematical concepts are reflected in real life. This is especially true for students who study physics, engineering and other technical disciplines, where linear algebra and analytical geometry play a key role. The author’s style is distinguished by clarity and logical presentation . Umnov A. E. He is able to explain complex things in simple language, which makes his books available to a wide audience. His other well-known works are also noteworthy as they continue to develop the themes touched upon in Analytical Geometry and Linear Algebra. Readers who are already familiar with his work will appreciate the consistency and depth with which the author approaches the study of mathematics. This book is not only useful for learning, but can also be an excellent resource for self-education. It will help develop critical thinking, logical reasoning and analytical skills, which is important in today's world, where mathematical skills are becoming increasingly in demand. If you are looking for something similar, pay attention to works such as "Linear Algebra and its Applications" D. X. Lyons or "Analytical Geometry" H. and . Lobachevsky . These books also offer an in-depth understanding of topics related to analytic geometry and linear algebra, and can be a great addition to your library. In conclusion, “Analytical Geometry and Linear Algebra” by Umnov A. E. is not just a textbook, but a real find for anyone who wants to understand mathematics at a deeper level This book will be your reliable helper on the way to knowledge, opening up new horizons for you in the world of numbers and forms. Do not miss the opportunity to get acquainted with this work - it will inspire you to new achievements and help you confidently step into the world of science.