Science and Education Publishing American Journal of Mechanical Engineering 2 7 2014 09 30 Theoretical Basics of Geometric Mechanics and Differential Geometry 178 183 EN Tomáš Lipták Department of Mechatronics, Faculty of Mechanical Engineering, Technical University of Košice, Košice, Slovakia Alexander Gmiterko Michal Kelemen Ivan Virgala Erik Prada František Menda AJME2014271 10.12691/ajme-2-7-1 2014 09 10 2014 09 17 2014 09 30 In this article are described the theoretical basics of geometric mechanics and differential geometry. In the introductory part of article, basic notions are explained that frequently occurring in the concept of geometric mechanics. It contains the basic building blocks that are used to create the configuration spaces. Further were described groups applied to the kinematic description of structure and to control in area of robotics and the fiber bundle that represents the configuration space for mechanical systems. The last part deals with the actions, such as the left and right action, lifted action and adjoint action.