The book "Linear Algebra: Methodical Guidelines", created by the team of authors, is an indispensable educational resource for students, teachers and everyone who seeks to understand the fundamental principles of one of the key disciplines of mathematics - linear algebra. This book is not just a collection of theoretical calculations, but a lively, rich in practical tasks and examples guide that helps to master complex concepts and apply them to real-world problems. The focus of Linear Algebra: Methodical Guidelines is not only classical topics such as vector spaces, matrices, systems of linear equations, eigenvalues and eigenvectors, but also modern approaches to their study. The authors, united by rich experience in teaching and research, tried to make the book as comprehensible and accessible as possible, while maintaining the academic rigor and completeness of the presentation. The reader will find here not only theoretical explanations, but also practical recommendations, exercises and methodological advice that greatly facilitate the process of learning and securing the material. Particular attention is paid to how to apply linear algebra in various fields - from engineering sciences and computer technology to economics and statistics. This makes the book particularly relevant to technical students, economists, programmers, and anyone facing the challenges of data analysis, modeling, and optimization. Thanks to a structured approach and clear explanations, even those who face this discipline for the first time will be able to quickly master the basic principles and move on to more complex topics. The book "Linear Algebra: Methodical Guidelines" is suitable for self-study, and will also be an excellent guide for teachers looking for effective teaching materials for conducting classes. It raises important topics such as the properties of matrices, their decomposition methods, the theory of linear transformations, as well as practical problems in finding solutions to systems of equations and analyzing their solutions. All this is accompanied by illustrations, diagrams and examples, which contributes to a deeper understanding of the material and the development of analytical thinking. The style of the authors is clear, logical and accessible, which makes the book pleasant to read even in an intensive educational process. The team of authors, known for their other textbooks on mathematics and computer science, created a work that not only teaches, but also inspires further study of mathematics, stimulating an analytical approach and critical thinking. If you are looking for a reliable source of knowledge in linear algebra that will help you prepare for exams, understand complex concepts or simply expand your mathematical horizons, “Linear Algebra: Methodical Guidelines” will be an excellent assistant for you. This book is a real guide to the world of linear structures, which will open up new horizons for you and make the study of mathematics fascinating and effective. It can be recommended to students of all levels, teachers, as well as those who appreciate a systematic approach and practical orientation in teaching.