The theorems of linear algebra, obtained in recent years and not included in the educational literature, but quite accessible to junior students, are presented with complete proofs. Non-standard elegant proofs of known theorems are also given. Written clearly, simply and clearly, the book brilliantly confirms the idea of ​ ​ the changeable appearance of linear algebra - this old branch of mathematics, constantly enriched in the process of solving specific problems. The new edition has been significantly revised and expanded compared to the previous one.