The book "Linear Algebra and Analytical Geometry: Study. A textbook for university students studying in the areas and specialties” by Alexander Sergeyevich Kirkinsky is not just a textbook, but a real find for students seeking to understand the basics of linear algebra and analytical geometry more deeply. In a world where mathematical concepts are becoming increasingly relevant in various fields of science and technology, this publication opens the door to understanding complex topics, making them accessible and understandable. The book covers a wide range of topics, ranging from the basics of linear algebra, such as vectors, matrices and systems of linear equations, to more complex concepts, including eigenvalues and eigenvectors. The author masterfully explains how these mathematical tools are used in analytical geometry, which allows readers not only to learn the theory, but also to see the practical application of knowledge. Each chapter is imbued with examples, tasks and illustrations that help to consolidate the material and develop analytical thinking. Who can like this manual? First of all, it is addressed to university students studying in areas related to mathematics, physics, engineering and computer science . However, due to the accessible style of presentation, the book will be interesting to those who just want to refresh their knowledge in the field of linear algebra and analytical geometry. It will become an indispensable assistant for teachers who want to supplement their lectures with high-quality material, as well as for independent researchers seeking a deep understanding of mathematical concepts. The topics raised in the book go beyond the simple study of formulas and algorithms. Kirkinsky focuses on the importance of mathematical thinking and logic, which makes this book particularly valuable in today's world, where critical analysis and problem-solving skills are becoming increasingly relevant. He emphasizes the connection between theory and practice, which allows readers not only to remember, but also to comprehend the material being studied. The style of Alexander Sergeyevich Kirkinsky is clear and logical He is able to explain complex things in simple language, which makes his books popular among students and teachers. There are already many other well-known works in his arsenal that also deserve attention. For example, his work on mathematical analysis and differential equations has been recognized for their accessibility and practical direction. If you are looking for a textbook that will not only teach you the basics of linear algebra and analytic geometry, but also inspire you to further study mathematics, then Kirkinsky’s Linear Algebra and Analytical Geometry is exactly what you need. This book will be your reliable companion on the way to the mathematical peaks, opening up new horizons of knowledge and opportunities for you. Do not miss the chance to immerse yourself in the world of mathematics with this fascinating and useful tutorial!