The current paper deals with analytical bunch compression studies for FLUTE whose results are compared to simulations. FLUTE is a linac-based electron accelerator with a design energy of approximately 40 MeV currently being constructed at the Karlsruhe Institute of Technology. One of the goals of FLUTE is to generate electron bunches with their length lying in the femtosecond regime. In the first phase this will be accomplished using a magnetic bunch compressor. This compressor forms the subject of the studies presented. The paper is divided into two parts. The first part deals with pure geometric investigations of the bunch compressor where space charge effects and the backreaction of bunches with coherent synchrotron radiation are neglected. The second part is dedicated to the treatment of space charge effects. The upshot is that the analytical results in the two parts agree quite well with what is obtained from simulations. This paper shall form the basis for future analytical studies of the FLUTE bunch compressor and of bunch compression, in general.