The quantum mechanics of singular systems is a topic of considerable importance for all the theories of elementary particle physics in which gauge invariance is a universal attribute. This is especially true for string theories which are gauge theories par excellence.
This thesis begins with a brief exposition of singular Hamiltonian mechanics. This tool is applied principally to manifestly supersymmetric particle and string theories. The Dirac particle and the bosonic particle and string are briefly examined. In particular, a method is shown for quantizing the point superparticle in four and ten dimensions. The two actions proposed for describing the manifestly supersymmetric string are shown to be essentially equivalent. The problems of their quantization are briefly discussed.
