This is a quite extraordinary book on Lie groups and algebraic groups. Created from hectographed notes in Russian from Moscow University, which for many Soviet mathematicians have been something akin to a "bible," the book has been substantially extended and organized to develop the material through the posing of problems and to illustrate it through a wealth of examples. Several tables have never before been published, such as decomposition of representations into irreducible components. This will be especially helpful for physicists. The authors have managed to present some vast topics: the...