Elements of Linear Algebra and Analytical Geometry: Studies . Karpov V . A. , Savina Yu. In. and Chopchiyan S. A. is an invaluable resource for students, faculty, and anyone interested in mathematics at a deeper level. This tutorial covers key aspects of linear algebra and analytic geometry, offering readers not only the theoretical knowledge but also the practical skills that are needed to successfully master these disciplines. The book begins with the basics, gradually deepening into more complex concepts. The authors have carefully worked out the material to make it accessible and understandable, even for those who are just beginning to get acquainted with mathematics. The manual deals with such important topics as vectors, matrices, systems of linear equations, as well as various methods of solving them. Particular attention is paid to geometric aspects, which allows readers to visualize abstract mathematical concepts and better understand their application in real life. This book will be especially useful for students of technical and natural science specialties, as well as for everyone who is preparing for exams in mathematics. It will be an excellent help for high school students who want to deepen their knowledge before entering the university. Teachers will also find in it a lot of useful materials that can be used in classes, as well as additional assignments for students. The topics raised in the book cover a wide range of issues, from basic concepts to more complex theories. The authors focus on the practical application of linear algebra and analytic geometry in various fields, such as physics, economics, and engineering. This makes the manual not only educational material, but also a reference for professionals working in these areas. Readers will be able to see how mathematical theories are applied to solve real-world problems, which adds practical value to the study. The style of the authors is distinguished by clarity and logical presentation, which makes the material easy to perceive. They skillfully combine theory with practical examples, which allows readers not only to memorize formulas, but also to understand how they work. In addition, the manual includes many tasks and exercises, which contributes to the consolidation of knowledge and the development of analytical thinking. If you are looking for similar works, you should pay attention to books such as "Linear Algebra and its Applications" D. Lyons or "Analytical Geometry" A. P. Kiseleva . These works also offer a deep dive into the world of mathematics, but the Elements of Linear Algebra and Analytical Geometry stands out for its structure and accessibility. In conclusion, "Elements of Linear Algebra and Analytical Geometry: Learning. The manual is not just a book, but a whole world of mathematical knowledge that is waiting to be discovered. It will become a reliable assistant on the way to mastering linear algebra and analytical geometry, as well as open the door to more complex mathematical concepts. Do not miss the opportunity to immerse yourself in the fascinating world of numbers and formulas that this manual offers.