Problems of nonholonomic mechanics, including many problems in robotics, wheeled vehicular dynamics and motion generation, have attracted considerable attention. These problems are intimately connected with important engineering issues such as path planning, dynamic stability, and , the investigation of many basic issues, and in particular, the role of symmetry in such problems, remains an important subject today. Despite the long history of nonholonomicmechanics, the establishment of pro- ductive links with corresponding problems in the geometric mechanics of systems with configuration-space constraints (., holonomic systems) still requires much development. The purpose of this work is to bring these topics closer together with a focus on nonholonomic systems with symmetry. Many of.