This volume is an outgrowth of the 1995 Summer School on Theoretical Physics of the Canadian Association of Physicists (CAP) held in Banff Alberta in the Canadian Rockies from July 30 to August 12 1995. The chapters based on lectures given at the School are designed to be tutorial in nature and many include exercises to assist the learning process. Most lecturers gave three or four fifty-minute lectures aimed at relative novices in the field. More emphasis is therefore placed on pedagogy and establishing comprehension than on erudition and superior scholarship. Of course new and exciting results are presented in applications of Clifford algebras but in a coherent and user-friendly way to the nonspecialist. The subject area of the volume is Clifford algebra and its applications. Through the geometric language of the Clifford-algebra approach many concepts in physics are clarified united and extended in new and sometimes surprising directions. In particular the approach eliminates the formal gaps that traditionally separate clas- sical quantum and relativistic physics. It thereby makes the study of physics more efficient and the research more penetrating and it suggests resolutions to a major physics problem of the twentieth century namely how to unite quantum theory and gravity. The term geometric algebra was used by Clifford himself and David Hestenes has suggested its use in order to emphasize its wide applicability and b& cause the developments by Clifford were themselves based heavily on previous work by Grassmann Hamilton Rodrigues Gauss and others.