Winner of the 2015 Prose Award for Best Mathematics Book!
In the fifth of his famous list of 23 problems, Hilbert asked if every topological group which was locally Euclidean was in fact a Lie group. Through the work of Gleason, Montgomery-Zippin, Yamabe, and others, this question was solved affirmatively. Subsequently, this structure theory was used to prove Gromov's theorem on groups of polynomial growth. In this graduate text, all of this material is presented in a unified manner.
