The book “Analytical Geometry and Linear Algebra”, created by the team of authors, is an indispensable educational resource for students, teachers and everyone who seeks to better understand the basics and intricacies of these important sections of mathematics. This book is not just a collection of theoretical formulas and definitions, but a lively and fascinating journey into the world of coordinate systems, vectors, matrices and multidimensional spaces, which reveals to the reader all the beauty and practical value of analytical geometry and linear algebra. What makes this book special? First, it combines the rigor of academic presentation with clarity and accessibility, which is especially important for those who are just starting out in mathematics or want to refresh their knowledge. The author's team carefully thought out the structure of the material so that each concept logically follows from the previous one, and complex topics, such as their own meanings, diagonalization or transformations in space, are revealed through living examples and understandable explanations. As a result, the book turns into not only a textbook, but also a source of inspiration for those who are looking for practical solutions in engineering, physics, computer science and other fields. This book is ideal for students of technical, mathematical and engineering specialties, as well as teachers looking for a modern and systematic manual for lectures and self-study. It will be especially useful for those who appreciate logical rigor, but do not want to lose interest in the subject. At the age of 16 years and older, readers will find here not only a theoretical basis, but also a variety of tasks, exercises and practical tasks that help to consolidate the material and prepare for exams or test papers. The topics raised in the book cover a wide range - from elementary concepts of coordinate systems and equations of lines and planes, to more complex issues related to matrices, systems of linear equations, vector spaces and their transformations. Particular attention is paid to visualization and geometric meaning, which makes the study more lively and understandable. The book also discusses algorithms and methods for solving practical problems, which emphasizes its applied nature and relevance in the modern world. The style of the authors is distinguished by clarity and accuracy, which makes complex topics available even to those who first encounter analytical geometry and linear algebra. In their works, there is a wealth of pedagogical experience and a desire to convey knowledge as clearly and interestingly as possible. The team of authors is famous for its textbooks and manuals, and “Analytical geometry and linear algebra” is a vivid confirmation of their professionalism and love for mathematics. This book is an excellent choice for those who want not only to memorize the formulas, but to understand how and why they work, to see the connection between abstract mathematical concepts and real problems. It will help develop analytical thinking, logical reasoning and the ability to solve complex problems, which makes it a valuable tool in the arsenal of any student and specialist. If you are looking for a tutorial that combines theory and practice, is clearly structured and filled with living examples, then “Analytical geometry and linear algebra” from a team of authors will become a reliable companion for you on the way to mathematical mastery. This book deserves attention not only because it covers all key topics, but also because it inspires further study and discovery of new horizons in the world of mathematics.