The Colour and Stereo Surface Imaging System (CaSSIS) is the scientific imager onboard the European Space Agency/Roscosmos ExoMars Trace Gas Orbiter. CaSSIS has one of the most advanced capabilities for colour imaging of the Martian surface on any spacecraft currently orbiting Mars. Such capability can only be utilized, however, by accurate geometric processing of CaSSIS datasets. Here we describe the dataset processing carried out by the CaSSIS geometry pipeline. This pipeline takes a number of single CaSSIS exposures and applies co-registration and map projection algorithms to produce full CaSSIS image mosaics in single and multiple wavelength bands. This process is described in detail along with the software packages that are implemented. The need for accurate co-registration between the different wavelength channels is shown. A description of the output from the pipeline is also given, with example images being shown to illustrate the result of using different CaSSIS wavelength channel combinations for image reconstruction.