Composition algebras and their generators.

The aim of this thesis is to show how the study of composition algebras and their generators has developed from a simple observation in logic made by Henry Maurice Sheffer nearly 60 years ago. The results in the algebra on 2 marks, which corresponds to classical 2-value sentence logic, were firmly established when Emil Post wrote a monograph on the subject 30 years ago. In this dissertation, however, they are developed in a more coherent and systematic way than has been attempted before and it is hoped that some novelty can be claimed for this exposition. More recent work has concentrated on the algebra on 3 marks (to which the author has made a published contribution) and on the general algebra. The outstanding problem in the general case has, in fact, been solved quite recently by Ivo Rosenberg. This thesis does not try to cover these later developments comprehensively; it concentrates on investigating and elucidating aspects of the subject that the author has found interesting and elegant.