The theory of algebraic invariants has found insufficient attention in Russian mathematical literature. The book by Alekseev , written in 1899, is largely out of date, while individual chapters in certain textbooks on algebra (Sushkevich, Bocher, etc.) written later, give only the beginnings of the theory.
A Practical Guide to the Invariant CalculusThis book explains recent results in the theory of moving frames that concern the symbolic manipulation of invariants of Lie group actions. In particular, theorems concerning the calculation of generators of algebras of differential invariants, and the relations they satisfy, are discussed in detail. The author demonstrates how new ideas lead to significant progress in two main applications: the solution of invariant ordinary differential equations and the structure of Euler-Lagrange equations and conservation laws of variational problems.
