The book "Elements of linear algebra and analytical geometry: methodological instructions for the implementation of control tasks" under the authorship of a team of authors, including E. C. Serebryannikova is an indispensable resource for students and teachers seeking a deeper understanding of the basics of linear algebra and analytical geometry. This edition is not just a manual, but a real find for everyone who wants to master these important sections of mathematics and put them into practice. The book contains methodological instructions that will help the reader not only to understand the theoretical aspects of linear algebra, but also to successfully complete control tasks. Each topic is presented with clear and accessible explanations, which makes the material understandable even for those who are just beginning to get acquainted with the subject. The reader is invited not only to study formulas and theorems, but also to apply them in practice, which contributes to the deep assimilation of material. This book will be especially useful for students of technical and natural sciences, as well as for anyone interested in mathematics and its applications. If you study at the Faculty of Physics, Computer Science, Engineering or in other related fields, the Elements of Linear Algebra and Analytical Geometry will become your reliable assistant in the educational process. It may also be of interest to teachers who are looking for quality teaching materials for their students. The topics raised in the book cover a wide range of issues, from the basics of vectors and matrices to more complex concepts such as linear transformations and their geometric interpretation. In each section, the authors focus on the practical application of the concepts studied, which helps the reader not only to remember the theory, but also to see its real value in various fields of science and technology. The book also includes many examples and challenges, making the learning process more interactive and engaging. The style of the authors is distinguished by clarity and logical presentation, which makes it easy to digest even the most complex topics. They use an accessible language, avoiding overly complex terms, which makes the book suitable for a wide audience. If you are familiar with other works E. C. Serebryannikova, you know that her approach to learning is always focused on the practical application of knowledge, which makes her books so popular among students. The book “Elements of Linear Algebra and Analytical Geometry” is not just a manual, but a whole methodological complex that will help you not only prepare for control tasks, but also lay a solid foundation for further study of mathematics. If you are looking for high-quality educational materials that will help you in mastering linear algebra and analytical geometry, this publication will be your faithful companion on the way to knowledge. Do not miss the opportunity to immerse yourself in the world of mathematics with this book, which will become your reliable assistant in learning and will help develop the analytical thinking necessary for a successful career in science and technology.