This introductory text, based on the authors long-standing teaching experience, aims to provide a basic preparation of fluid dynamics, with particular attention to the dynamics of the oceans and the atmosphere, which require consideration of the Coriolis force. The most salient features of this text are its simplicity and compactness. As for simplicity, much attention has been paid to the connections between the various topics, not skimping on simple and intuitive explanations, so that the reader can easily acquire a unitary vision of the subject. As for its compactness, this is evident in the limited, yet sufficiently broad, range of topics analyzed, considered fundamental. This text is, therefore, particularly suitable for a wide audience of upper undergraduate students, but it also constitutes a valuable resource for masters and doctoral students, as well as to researchers who carry out their scientific activity in the broad context of meteorology, oceanography, and climatology.