Nonholonomic systems are a common theme in many scientific and economic fields, including robotics, motion and space exploration. This work sheds new light on this interdisciplinary investigation by a number of elements from different disciplines. The main goal is the idea that a better understanding of the geometric structure of new aspects of the mechanical systems and unknown to them to illustrate shows and helps both the analysis and design to solve problems in the feet and to identify new challenges. In this way the different areas of research such as classical mechanics, differential geometry, Numerical Analysis and Control Theory are collected in this study of Nonholonomic Systems. 