In this book the author expounds linear algebra and geometry through tensor calculus trying to underline the invariance of the main notions and results. The discussions and explanations of the notions and theorems precede to their strong definitions and proofs. The author also considers the themes connected with groups of transformations and invariant theory: representations of the group $GL(n,K)$ and the orthogonal group $0(n,K)$, problems of classification of tensors (symmetric and skewsymmetric) and linear transformations of vector spaces. He expounds classical problems of tensor algebra and representation theory of groups and Lie algebras. The book containes the following main themes: representations of the symmetric group and decomposition of tensor space; representations of semisimple Lie algebras; elements of invariant theory of tensors: homogeneous spaces and representation theory; tensors in the three- dimensional Euclidean space (representations of the Lie algebra $sl(2,{\bbfC})$, invariants of representations of the Lie algebra $sl(2,{\bbfC})$.
Reviewer: N.I.Osetinski (Moskva)