Construction of MV polytopes via LS galleries The result of this thesis is a connection between the LS galleries model for finite dimensional representations of a complex simply connected semi simple algebraic group G as introduced by Gaussent and Littelmann and MV polytopes (short for Mirkovic and Vilonen) via retractions in the affine building. MV polytopes were studied by Anderson and Kamnitzer they are the images of MV cycles under the moment map. It is well known that both the LS gallery model as well as the MV polytopes give a combinatorial realisation of finite dimensional representations of G. In this thesis we give a combinatorial method to relate these two models. This is done by constructing starting from a given LS gallery a set of combinatorial galleries whose endpoints span the corresponding MV polytope. We show that these galleries are exactly the images of the associated Bialynicki Birula cell under suitable retractions of the affine building.