The book "Elements of linear algebra and tensor calculus with the application of methods for solving typical problems" by Yuri Pavlyuchenko and Valery Ryzhkov is not just a textbook , A real find for students, Post-graduate students and all , who seeks to better understand the basics of linear algebra and tensor calculus. This publication will become a reliable assistant for those who study mathematics at the level of higher education, as well as for teachers looking for quality material for preparation for classes. The book covers a wide range of topics, ranging from basic concepts of linear algebra, such as vectors, matrices and systems of linear equations, to more complex concepts of tensor calculus. The authors masterfully explain how these mathematical tools are used in various fields of science and technology, which makes the material not only theoretically significant, but also practical. The reader will be able to see how linear algebra and tensors affect real-world problems in physics, engineering, and even economics. For whom is this manual intended? First of all, the book will be useful for students of technical and natural sciences specialties, as well as for those who are preparing for exams in mathematics . It will be a great help for teachers who are looking for quality materials for their courses. In addition, the book may be of interest to anyone who is fond of mathematics and wants to expand their knowledge in this area. Even if you are not a student, but want to understand the basics of linear algebra and tensor calculus, this guide will be an excellent start. What makes this book particularly appealing is its practical focus. The authors not only present theoretical aspects, but also offer methods for solving typical problems, which allows the reader not only to assimilate the material, but also to apply it in practice. Each chapter includes examples that help to consolidate what has been learned, as well as tasks for self-decision, which contributes to a deeper understanding of the topic. The style of the authors is distinguished by clarity and accessibility, which makes even the most complex concepts understandable to a wide audience. Yuriy Pavlyuchenko and Valery Ryzhkov are experienced teachers who know how to convey information to students . Their approach to learning is based on many years of experience, which makes this manual not only informative, but also fascinating. If you are looking for books on linear algebra, tensor calculus or mathematics in general, then “Elements of linear algebra and tensor calculus” will be an excellent choice. It can be compared to other well-known textbooks, such as David Lyons' Linear Algebra and its Applications or