This textbook provides an essential introduction to Lie groups,
presenting the theory from its fundamental principles. Lie groups
are a special class of groups that are studied using differential
and integral calculus methods. As a mathematical structure, a Lie
group combines the algebraic group structure and the differentiable
variety structure. Studies of such groups began around 1870 as
groups of symmetries of differential equations and the various
geometries that had emerged. Since that time, there have been major
advances in Lie theory, with ramifications for diverse areas of
mathematics and its applications. Each chapter of the book begins
with a general, straightforward introduction to the concepts
covered; then the formal definitions are presented; and
end-of-chapter exercises help to check and reinforce comprehension.
Graduate and advanced undergraduate students alike will find in
this book a solid yet approachable guide that will help them
continue their studies with confidence.
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