The book "Linear Spaces and Linear Displays: A Training Manual" by the authors Skvortsov M. and . , Antonova I. In. , Ratnova A. G. and Solomon's E. In. is a valuable guide for undergraduates, graduate students and anyone interested in linear algebra and its applications. This edition not only covers the theoretical foundations of linear spaces and linear mappings, but also offers the reader a deep understanding of these concepts through practical examples and tasks. At the heart of the book is the study of linear spaces, a key element in mathematics that finds application in a wide variety of fields, from physics to economics. The authors masterfully explain what linear combinations, bases and dimensions are, and also consider important properties of linear maps. Each chapter is designed to gradually deepen the reader’s knowledge, starting with simple concepts and moving on to more complex topics. This makes the book suitable for both beginners and those who already have basic knowledge in this field. Who can like this tutorial? First of all, it will be useful for students of mathematical and engineering specialties, as well as for those who study related disciplines, such as physics and computer science . The textbook will become an indispensable assistant for teachers who are looking for quality materials for their courses, as well as for self-taught students seeking to deepen their knowledge in linear algebra. If you are interested in mathematics, want to develop analytical thinking, or are just looking for a way to improve your problem solving skills, this tutorial will be an excellent choice. The topics raised in the book go beyond purely mathematical concepts. The authors focus on the practical application of linear algebra in various fields, such as computer graphics, data processing, and even economics. This allows the reader to see how abstract mathematical concepts find their application in the real world, making the study more fascinating and meaningful. The style of the authors is clear and accessible. Each section of the book is accompanied by many illustrations and examples, which helps to better absorb the material. The authors aim to make complex ideas accessible to understanding, which is an important aspect in academic literature. In addition, the manual contains many tasks of varying complexity, which allows the reader not only to consolidate the knowledge gained, but also to develop the skills of their application. If you are looking for literature on linear algebra that combines theory and practice, then “Linear Spaces and Linear Displays: A Tutorial” will be a real find for you. This is not just a textbook, but a whole world in which mathematics comes to life, and its principles become understandable and accessible. The book may also be of interest to those who are passionate about mathematical modeling and want to understand how linear spaces can be used to solve real-world problems. Do not miss the opportunity to immerse yourself in the fascinating world of linear algebra with this wonderful guide. It will become your reliable companion in the study and will help open new horizons in understanding mathematics and its application in life.