||The monograph is devoted to a development and an improvement of models and methods for studying problems of vortex and wave dynamics. The book contains an all-sufficient yet relatively elementary insight into that which is named in modern scientific literature the Hamiltonian approach as applied to hydrodynamic models in general and to geophysical fluid dynamics in particular. This monograph is a significant upgrade in comparison with the book «Problems of fluid dynamics in Hamiltonian descriptions»  published by the same authors in 1993. First, the Hamiltonian approach is considered in a broader context and as a tool to create new more effective models and asymptotic methods. Second, the book includes the latest advances in applications. In particular, it contains new sections devoted to the Hamiltonian approach for hydrodynamic models of plasma, fluid crystals, contour dynamics and anisotropic wave systems. Special attention is given to the large-scale wave and vortex structures, which are important for understanding processes of vertical and horizontal mixing in the atmosphere and the ocean. Theoretical results presented in the monograph are of general physical interest and can find a wide use in the theory of hydrodynamic stability, turbulence and dynamic meteorology.
The book is suitable for researchers specializing in fluid dynamics and its applications, theoretical
and mathematical physics, applied mathematics as well as for post-graduate and advanced students