This monograph is devoted to the problem of inferring geometric information about arbitrarily curved surfaces from visual cues; this is a central problem in computer vision with immediate relevance for robot manipulation and navigation.<BR>The author develops computational theories and techniques relating visual information arising from viewer movements to the differential geometry of visible surfaces. The theories developed have been implemented and tested using a real-time tracking system based on deformable contours. Applications of the techniques to geometric modelling, obstacle avoidance, navigation, and object manipulation are presented.