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The book provides some recent works in the study of some infinite-dimensional dynamical systems in atmospheric and oceanic science. It devotes itself to considering some infinite-dimensional dynamical systems in atmospheric and oceanic science, especially in geophysical fluid dynamics. The subject on geophysical fluid dynamics mainly tends to focus on the dynamics of large-scale phenomena in the atmosphere and the oceans. One of the important contents in the dynamics is to study the infinite-dimensional dynamical systems of the atmospheric and oceanic dynamics. The results in the study of some partial differential equations of geophysical fluid dynamics and their corresponding infinite-dimensional dynamical systems are also given.