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All Rights Reserved iii Acknowledgements I want to thank my fiancee, Lisa, for her understanding and support these past months while this dissertation was written. I also thank my family for their support and encouragement these many years. My good friend and coauthor of two papers, Phil Rosenthal, deserves special recognition for his contributions to our discussions and research in both fractional superstrings and stringy cosmology. Rakhmanov, additionally contributed much to the stimulating and enjoyable research atmosphere at Caltech, as did all the other graduate students, postdoc's and senior faculty on the fourth floor. I also thank David Lewellen for spurring my interest in higher level KM algebras with his 1989 paper, [1] and for the opportunity of working together on the paper [2] that forms much of chapter three of this thesis. I also want to recognize those people outside of Caltech, with whom discussions, on issues relevant to this thesis, were very rewarding. This list includes Phil Argyres, and Keith Dienes. Several others merit thanks for discussions on various issues of string cosmology: deserves special thanks for his guidance of my research. I thank him for the opportunity to carry on an apprenticeship into elementary particle physics and string theory under his supervision. Lastly, I want to recognize Helen Tuck for the help she so kindly gives in her role as secretary of the particle theory group. iv To Lisa v With regard to strings: For a theory may be formed by the mind, and therefore be shaped by its structures. However, it frequently happens that the descriptive power of a good theory so transcends the meager understanding of the original conception, that is is very hard to believe that the theory only reflects our cognitive structures. It would then appear to be in much closer contact with nature than with our minds; our minds are continually agasped at its applicability. Abstract The focus of this thesis is on (1) the role of Kač-Moody algebras in string theory and the development of techniques for systematically building string theory models based on higher level (K ≥ 2) KM algebras and (2) fractional superstrings, a new class of solutions based on SU (2) K /U (1) conformal field theories. The content of this thesis is as follows. In chapter two we review KM algebras and their role in string theory. In the next chapter, we present two results concerning the …