This is the first book to provide a systematic explanation of both
the problems of symplectic topology, and analytical details and
techniques in applying the machinery embedded in the Floer theory
as a whole. It provides a self-contained exposition of all
foundational materials of Floer theory and its applications to
various problems arising in symplectic topology. The author gives
complete analytic details assuming the reader's knowledge of basic
elliptic theory of (first-order) partial differential equations,
second-year graduate differential geometry and first-year algebraic
topology. He motivates various constructions appearing in Floer
theory from the historical context of Lagrange Hamilton's
variational principle and Hamiltonian mechanics. He also provides
100 exercises so that readers can test their understanding. The
book is a comprehensive resource suitable for experts and newcomers
alike."
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