The book “Linear Algebra and Analytical Geometry . Theory and Practice: A Study Guide” by a team of authors, including D. Z. Ilyazov is an indispensable resource for students and teachers seeking a deeper understanding of the basics of linear algebra and analytical geometry. This tutorial not only covers the theoretical aspects of these disciplines, but also offers practical tasks that allow you to consolidate the knowledge gained . The book focuses on key concepts of linear algebra, such as vectors, matrices, systems of linear equations and their solutions. Readers will be able to get acquainted with the basics of analytical geometry, including the study of planes and spatial figures. Each section of the book is carefully structured, which makes it easy to navigate the material and find the necessary information. Interestingly, the authors emphasize the relationship between linear algebra and geometry, which helps readers see the practical application of the theories studied. This book will be especially useful for students of technical and natural science specialties, as well as for anyone interested in mathematics and its applications in various fields. It is suitable for both beginners and those who already have basic knowledge and want to deepen their skills. Teachers will find in it a rich material for preparing for classes and developing curricula, as well as many examples and tasks for independent work. Topics that are raised in the book range from the basics of linear algebra to more complex concepts such as eigenvalues and eigenvectors. The authors emphasize the importance of these concepts in various scientific and engineering disciplines, such as physics, economics, and computer science. The book also considers the application of linear algebra in modern technologies, which makes it relevant for students seeking to work in the field of IT and engineering. The style of presentation of the authors is clear and accessible, which allows readers to easily absorb even the most complex ideas. They use many real-life examples to illustrate how linear algebra and analytic geometry are applied in practice. This makes the study of the material not only useful, but also fascinating. The book “Linear Algebra and Analytical Geometry . Theory and Practice" is part of an extensive series of teaching aids that cover various aspects of mathematics and its applications. Other well-known works by authors also deserve attention as they continue to develop the topics raised in this textbook and offer readers new horizons to explore. If you are looking for a high-quality tutorial on linear algebra and analytical geometry, which will help you not only to master the theory, but also to apply it in practice, then this publication will be an excellent choice. It is suitable for students, schoolchildren, teachers and anyone who wants to deepen their knowledge in mathematics. Do not miss the opportunity to discover the world of linear algebra and analytical geometry with this fascinating and informative guide!