This volume consists of 24 lectures delivered at a workshop on long-time predictions in nonlinear conservative dynamical systems organized by the Center for Studies of Statistical Mechanics, the Center for Orbital Dynamics, and the Institute for Fusion Studies at the University of Texas at Austin. The organization of the lectures reflects this cooperative effort and is divided into four parts: Statistical Mechanics, Dynamics, Plasma Physics, and Beam-Beam Interactions. The recurrent theme in each of these areas of investigation is the determination of the general conditions for the onset of chaotic behavior in nonlinear systems, i.e., predictability and chaos are the two sides of the same coin. Thus, the predictability content of most of the lectures is implicit rather than explicit; it is assumed that measures for the onset of chaos and the growth rate of instabilities are sufficient indicators of predictability or rather its loss. Direct measures of predictability such as the variance of the error field used in meteorology were not discussed.