Encuadernaci� carton�The theory of Lie groups relies on Cartan's theorem on the equivalence of the category of simply connected Lie groups to that of Lie algebras. This book presents the proof of the Cartan theorem and the main results. The branches of the theory of Lie groups which rest on the Cartan theorem remain outside the limits of our exposition. The theory of Lie algebras has been developed to an extent necessary for the Cartan theorem to be proved.This book like the previous ones of this series* is a nearly faithful record of the Lectures delivered by the author at Moscow University to students (and postgraduates) of the Faculty of Mathematical Mechanics. However, while books I and II were based on Lectures of a compulsory course, this book is a record of an elective course, which makes it essentially different in a number of respects.

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