A text for graduate students with previous courses in analysis and linear algebra, introducing the idea of the formalism of simplectic forms, the simplectic group, and simplectic manifolds. Demonstrates connections between mathematical objects and the formalism of theoretical mechanics, in particular the Hamiltonian formalism, and that of the quantum formalism, namely the process of quantization. Extensive appendices offer definitions and mathematical groundwork. Annotation c. Book News, Inc., Portland, OR (booknews.com)