The structure of compact groups : a primer for the student a handbook for the expert Publisher’s description: The subject matter of compact groups is frequently cited in fi elds like algebra topology functional analysis and theoretical physics. This book serves the dual purpose of providing a text for upper level graduate students and of being a source book for researchers who need the structure and representation theory of compact groups. After a gentle introduction to compact groups and their representation theory the book presents self contained courses on linear Lie groups and on locally compact abelian groups.Appended chapters contain the material for self contained courses on abelian groups and on category theory.Using the Lie algebras and the exponential function of arbitrary compact groups the book avoids unnecessary restrictions to finite dimensional or abelian compact groups. Earlier editions of 1998 2006 2013 and 2020 have been quoted for instruction and research. The present edition conceptually sharpens polishes and improves the earlier material. For instance it includes a treatment of the Bohr compactifi cation of topological groups which fi ts perfectly into the general treatment of adjoint functors that the book treats in an appendix of its own and which in the abelian environment connects neatly with the Pontryagin van Kampen duality of compact abelian groups having been discussed in the book in great detail. The link between arbitrary compact groups and their weakly complete group algebras is as extensively discussed as is now the theory of weakly complete universal enveloping algebras of the Lie algebras of compact groups. All of this is based on the category of weakly complete real and complex vector spaces and its precise duality to the category of ordinary real respectively complex vector spaces is treated in an appendix systematically. *Thorough introduction to compact groups which have applications in algebra topology functional analysis and theoretical physics. *Thrust of the book points to structure theory of infinite dimensional not necessarily commutative compact groups.