This work deals with the foundations of classical physics from the ``symplectic`` point of view, and of quantum mechanics from the ``metaplectic`` point of view. The Bohmian interpretation of quantum mechanics is discussed. Phase space quantization is achieved using the ``principle of the symplectic camel``, which is a recently discovered deep topological property of Hamiltonian flows. The mathematical tools developed in this book are the theory of the metaplectic group, the Maslov index in a precise form, and the Leray index of a pair of Lagrangian planes. The concept of the ``metatron`` is introduced, in connection with the Bohmian theory of motion. A precise form of Feynman`s integral is introduced in connection with the extended metaplectic representation.

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