CARS is a program for defining Möbius transformations and Riemann surfaces for computations with other programs. CARS can be used to define hyperbolic Möbius transformations in a geometric way by specifying their fixed-points and their multiplier. CARS can show the axis of these transformations and the respective isometric circles. CARS can also display Möbius transformations that have been written as words of other transformations. Using Combination Theorems, CARS can build Fuchsian groups corresponding to any compact Riemann surface. These groups can further be deformed by the Fenchel-Nielsen twist, for instance.