This delightfully idiosyncratic work is a welcome addition to the literature on Lie groups. In contrast to many of the polished texts on the topic, which present the subject as if it had sprung, fully mature, from the heads of one or other of the olympian scholars who have moulded it, these tomes introduce first matrix groupsand then general Lie groups. Godement begins with topological groups, covering groups, and linear groups, and describes, hands-on, the relation between Lie algebras and Lie groups for the matrix groups and their covering groups. He later introduces manifolds, abstract Lie groups, and the differential geometric approachto the connection between Lie groups and algebras. The reader, fore-warned that general Lie groups are in fact no more than covering groups or matrix groups, is enabled to handle the abstract theory with confidence by having already understood the concrete approach. [...]Students could do much worse than to work their way through, and for the advanced, the occasional insight, the fresh points of view, and the author's mordant asides make it a worthwhile read. Recommended.

M. Cowling in ZentralblattMath