The motivation for this North Atlantic Treaty Organization (NATO) Advanced Study Institute (ASI) came from the fact that a hierarchy of physically based mathematical models of the earth's climate has been and is being developed to quantitatively investigate the earth's past, present, and potential future climates. These models are currently being applied, for example, to understand the causes of the ice ages that have occurred with a period of about 100,000 years during the last million years, to study the predictability of climate on the time scale of 1-3 months (with particular attention on the worldwide El Niño phenomena), and to project the potential climatic consequences of the increasing concentration of atmospheric CO2 and other trace gases. These studies are showing great potential toward the development of a comprehensive theory of climate. However, the development, testing, and application of mathematical climate models requires the dedicated efforts of an increasing number of specially trained and highly motivated scientists. The objective of the AS1 was to provide this training and motivation through a course taught by internationally recognized experts on physically based modeling and simulation of climate and climatic change.