We investigated how the CNS learns to control movements in different dynamical conditions, and how this learned behavior is represented. In particular, we considered the task of making reaching movements in the presence of externally imposed forces from a mechanical environment. This environment was a force field produced by a robot manipulandum, and the subjects made reaching movements while holding the end-effector of this manipulandum. Since the force field significantly changed the dynamics of the task, subjects' initial movements in the force field were grossly distorted compared to their movements in free space. However, with practice, hand trajectories in the force field converged to a path very similar to that observed in free space. This indicated that for reaching movements, there was a kinematic plan independent of dynamical conditions. The recovery of performance within the changed mechanical environment is motor adaptation. In order to investigate the mechanism underlying this adaptation, we considered the response to the sudden removal of the field after a training phase. The resulting trajectories, named aftereffects, were approximately mirror images of those that were observed when the subjects were initially exposed to the field. This suggested that the motor controller was gradually composing a model of the force field, a model that the nervous system used to predict and compensate for the forces imposed by the environment. In order to explore the structure of the model, we investigated whether adaptation to a force field, as presented in a small region, led to aftereffects in other regions of the workspace. We found that indeed there were aftereffects in workspace regions where no exposure to the field had taken place; that is, there was transfer beyond the boundary of the training data. This observation rules out the hypothesis that the subject's model of the force field was constructed as a narrow association between visited states and experienced forces; that is, adaptation was not via composition of a look-up table. In contrast, subjects modeled the force field by a combination of computational elements whose output was broadly tuned across the motor state space. These elements formed a model that extrapolated to outside the training region in a coordinate system similar to that of the joints and muscles rather than end-point forces. This geometric property suggests that the elements of the adaptive process represent dynamics of a motor task in terms of the intrinsic coordinate system of the sensors and actuators.