This thesis is concerned with the application of neutron and X-ray diffraction techniques to the study of hydrogen bonding in the acid salts of some simple carboxylic acids and, in particular, those of glutaric acid. It is divided into three parts. By way of introduction, Part 1 contains a brief review of the subject of hydrogen bonding with emphasis on symmetrical hydrogen bonds and on the deuterium isotope effect. This is followed by a review of the available structural data for the acid salts of dicarboxylic acids. The elucidation, by X-ray diffraction analyses, of the crystal structures of potassium hydrogen glutarate, potassium hydrogen di-m-chlorobenzoate and potassium trihydrogen diglutarate is described in Part 2. The first two salts possess very short (2.445 A and 2.437 A respectively) crystallographically symmetrical hydrogen bonds while the last is an acid salt of a novel type. The structures of all three are discussed. A comparison of the crystal structures of potassium hydrogen ditrifluoroacetate and its deuteriate as determined by neutron diffraction analyses is made in Part 3 and the result adduced as evidence of genuine symmetry in the short (2.437 A) hydrogen bonds. As well as a discussion of these crystal structures, the application of the "difference-Patterson" function to neutron diffraction data is examined and is found to constitute a valid method for phase determination. This part is concluded with the description of the neutron diffraction analyses of potassium and ammonium hydrogen glutarate both of which confirm the X-ray results but locate the hydrogen atoms more precisely. Finally, the thesis contains two appendices; the first is a published paper describing and comparing the crystal structures of rubidium and ammonium hydrogen glutarate while the second is concerned with the effects of extinction in neutron and X-ray diffraction analyses and contains programs developed for the correction of the errors arising from this effect.