The book "Analytical geometry and linear algebra" by Umnov A. E. It is a fascinating and deep dive into the world of mathematical concepts that play a key role in modern education and research. This work will become an indispensable assistant for both students and teachers seeking a deeper understanding of these important disciplines. In this book, the author masterfully combines theory and practice, which allows the reader not only to learn the basic principles of analytical geometry and linear algebra, but also to see their application in real-world problems. Umnov A. E. offers the reader a unique approach to learning, which includes many examples, tasks and illustrations, making the learning process more visual and accessible. Each chapter of the book is imbued with logic and consistency, which makes it easy to move from one topic to another without losing the thread of the narrative. The book will be of interest to a wide range of readers: from students preparing for exams to university students studying mathematics at a deeper level. It will also be useful for teachers who are looking for new approaches to explaining complex topics. If you are passionate about mathematics, want to develop your analytical skills or are just looking for a way to improve your knowledge in the field of geometry and algebra, this publication will be a real find for you. The topics raised in the book cover a wide range of issues ranging from the basics of analytic geometry, such as coordinate systems and equations of straight lines and planes, to more complex concepts of linear algebra, including vectors, matrices, and systems of linear equations. Umnov not only explains the theory, but also shows how these mathematical tools can be used to solve practical problems in various fields, such as physics, engineering, and economics. The style of Umnov is distinguished by clarity and accessibility, which makes his work especially valuable for those who are faced with mathematics for the first time or have difficulties in mastering it. The author uses simple and understandable examples that help the reader to better assimilate the material. His approach to learning is based on the principle of “from simple to complex”, which allows you to gradually delve into the topic without losing interest and motivation. In addition, Umnov A. E. He is known for his other work in mathematics and education, and his experience in teaching is reflected in every page of this book. Readers familiar with its previous editions will appreciate the consistency and depth of its presentation, and beginners will be able to discover the amazing world of analytical geometry and linear algebra. If you are looking for books on mathematics that will help you understand complex topics, or want to find a tutorial for preparing for exams, "Analytical geometry and linear algebra" Umnova A. E. It will be a great choice.. This work will not only enrich your knowledge, but also inspire you to further study mathematics, opening up new horizons and opportunities for you. Do not miss the chance to immerse yourself in this fascinating world of numbers and shapes, which will undoubtedly change your perception of mathematics forever.