Customer Reviews

Lectures on Symplectic Geometry (Lecture Notes in Mathematics)

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I disagree with the previous reviewer. This is the most accessible text I know on symplectic geometry, and the one I would recommend to a beginning graduate student trying to learn the topic on their own. It is certainly easier (and lighter) than McDuff and Salamon's book (Introduction to Symplectic Topology), which is much more comprehensive but requires more effort.

On the one hand, it's a good and fairly complete book on modern symplectic geometry and Hamiltonian systems, but on the other hand it is extremely dense without any illuminating examples, which makes reading it very difficult. Unfortunately, the concise lecture notes style is typical in mathematics today, so there aren't many alternatives if you want a book that deals with most of the theory.

In order to read and understand the book you probably have to be an advanced graduate student in mathematics with a clear affinity towards minimalistic, sentence-free lemma-proof-theorem-proof texts. As a textbook I cannot recommend these Lectures on Symplectic Geometry, as they are too dense, too proof-oriented and too example-devoid. As a quick reference for young researchers in mathematics who already master the rudiments of symplectic topology and geometry it might be an inexpensive possibility. For all others (the actually intended audience, i.e. the interested students who want to learn about symplectic geometry) it is a non-risk-free investment: you have to take the time and go very slowly through the material and either you are rewarded for your great efforts eventually or you are stuck at trivialities and become discouraged unduly.