Lie Algebras and Locally Compact Groups

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This volume presents lecture notes based on the author's courses on Lie algebras and the solution of Hilbert's fifth problem. In chapter 1, "Lie Algebras, " the structure theory of semi-simple Lie algebras in characteristic zero is presented, following the ideas of Killing and Cartan. Chapter 2, "The Structure of Locally Compact Groups, " deals with the solution of Hilbert's fifth problem given by Gleason, Montgomery, and Zipplin in 1952.