The book "Linear Algebra: A Textbook: For Universities" by Ilyin V. A. and Poznyak E . G. It is a thorough and comprehensive guide to one of the key disciplines in mathematics that finds its application in a wide variety of fields of science and technology. This textbook will become an indispensable assistant for students, graduate students and anyone who seeks to better understand the basics of linear algebra and its practical application. Linear algebra is not just a set of formulas and theorems, but a whole philosophy that allows you to describe and analyze a variety of phenomena, from the simplest geometric shapes to complex systems in physics and economics. Authors, B. A. Ilyin and E. G. Lately, with great attention and care, they approached the presentation of the material, emphasizing an intuitive understanding of the concepts, which is especially important for students who are just starting their way in studying mathematics. They offer the reader not only theoretical foundations, but also many practical problems that will help to consolidate the knowledge gained. The book covers a wide range of topics, ranging from vectors and matrices to eigenvalues and linear transformations. Each section is built logically and consistently, which allows the reader to easily navigate the material and not lose the thread of reasoning. The authors use many examples from real life, which makes the study of linear algebra more exciting and accessible. This is especially important for students who may encounter difficulties in perceiving abstract concepts. The textbook will be particularly useful for students of technical specialties such as computer science, physics, engineering, and economics. However, it can also be of interest to a wider audience from students preparing for exams to teachers looking for quality material for their courses. The book is suitable for self-study, thanks to clear explanations and a variety of tasks that will help the reader to test their knowledge and skills. One of the key topics raised in the book is the connection of linear algebra with other areas of mathematics and science.[citation needed] The authors emphasize how linear algebra serves as the basis for the study of more complex mathematical concepts, such as analysis and differential equations. This makes the textbook not only useful, but also necessary for the formation of a holistic understanding of mathematics as a science. The style of the authors is clear and accessible, which makes even the most complex topics understandable. Ilyin V. A. and Pozniak E. G. experienced teachers and researchers who know how to convey information to students . Their previous work has also received recognition in the academic environment, and this textbook was no exception. It is the result of many years of experience and in-depth research in the field of linear algebra. If you are looking for a high-quality textbook on linear algebra, which will help you not only to master the theory, but also to learn how to apply it in practice, "Linear algebra: Textbook: For universities" will be an excellent choice. It will not only expand your knowledge, but also help develop analytical thinking, which is an important skill in the modern world. Do not miss the opportunity to immerse yourself in the fascinating world of linear algebra with this wonderful textbook!