Jürgen Moser (1928–1999) was one of the most accomplished mathematicians of the second half of the 20th century and his work had a major impact in broad areas of analysis, especially partial differential equations and dynamical systems, and geometry. In this article we discuss only his contributions to dynamics and closely related areas. We feel that the best way to make the reader understand and appreciate the impact of Moser's work is to discuss it within the framework of some major trends in the development of dynamical systems during the last century. We apologize in advance for omitting many important references, including some key original work. These can be found in secondary sources to which we refer for detailed accounts of various areas. Needless to say, we included in our references all papers by Moser relevant to our discussion. For brief surveys of Moser's work in all areas see [45,91].

The leading theme of virtually all of Moser's work in dynamics is the search for elements of stable behavior in dynamical systems with respect to either initial conditions or perturbations of the system.