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This work incorporates three modern aspects of mathematical physics: the jet methods in differntial geometry, the Lagrangian formalism on jet manifolds and the multimomentum approach to the Hamiltonian formalism. Several contemporary field models are investigated in detail. This is not a book on differential geometry, although modern concepts of differential geometry are used throughout the book. Quadratic Lagrangians and Hamiltonians are studied on the general level including the treatment of Hamiltonian formalism on composite fibre manifolds. The book presents new geometric methods and...

The geometric formulation of autonomous Hamiltonian mechanics in the terms of symplectic and Poisson manifolds is generally accepted. This book provides the geometric formulation of non-autonomous mechanics in a general setting of time-dependent coordinate and reference frame transformations.

Contemporary quantum field theory is mainly developed as quantization of classical fields. This book aims to provide a mathematical foundation of Lagrangian classical field theory and its BRST extension for the purpose of quantization. It considers reducible degenerate Lagrangian theories of even and odd fields on an arbitrary smooth manifold.

- The book collects all the advanced methods of quantization in the last decade.
- It presents in a compact way all the necessary up to date mathematical tools to be used in studying quantum problems.