The fusion of two biological membranes is an important step in many processes on the cellular and sub-cellular level. Understanding the involved interplay of different lipid species, a specialized protein machinery and water on length scales of few nanometers poses a significant challenge to current structural biology. Among several complementary approaches, one strategy is to study the structural rearrangements of the lipid matrix. As the initial step, lipid bilayers must be forced into close contact to form a non-bilayer intermediate termed a stalk. This has been the subject of numerous theoretical studies and simulations, but experimental data on stalks are largely lacking. Currently, the only way to obtain structural information at the required sub-nanometer resolution is x-ray diffraction on the recently discovered “stalk phase” formed by certain lipids. We apply this method to elucidate the effect of lipid composition on stalk geometry and the repulsive forces between lipid bilayers prior to stalk formation. An approach based on differential geometry of electron density isosurfaces is introduced to analyze the curvatures and bending energies of the lipid monolayers. For the first time, this connects experiment-based structures of stalks and the associated bending and hydration energies. In addition, this thesis aims to provide a self-contained introduction to the required background in x-ray diffraction on lipid mesophases and electron density reconstruction.