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."

The advent of relatively inexpensive but powerful computers is af fecting practically all aspects of our lives, but some of the greatest influence is being felt in the physical sciences. However, university curricula and teaching methods have responded somewhat cautiously, having only recently come to terms with the now omnipresent calcula tor. While many instructors at first feared that the widespread use of pocket calculators would lead to generations of students who could not multiply or perhaps even add, few now seriously lament the disappear ance of slide rules, logarithm tables, and the often error-bound tedium that such tools of the trade demand. Time that used to be spent on the use of logarithm tables and manual square-root extraction can be prof itably turned to earlier studies of calculus or computer programming. Now that the calculator has been accepted into the classroom, we face a computer-software revolution which promises to be considerably more profound. Modern textbooks in the physical sciences routinely assume their readers have access not only to calculators, but often to home or even mainframe computers as well, and the problems teachers discuss and assign students can be more complex and often more realistic than in the days of only pad and pencil computations. As less effort is spent on numerical computation, more can be devoted to conceptual under standing and to applications of the increasingly sophisticated mathe matical methods needed for a real appreciation of recent advances in the discipline."

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."

The advent of relatively inexpensive but powerful computers is af fecting practically all aspects of our lives, but some of the greatest influence is being felt in the physical sciences. However, university curricula and teaching methods have responded somewhat cautiously, having only recently come to terms with the now omnipresent calcula tor. While many instructors at first feared that the widespread use of pocket calculators would lead to generations of students who could not multiply or perhaps even add, few now seriously lament the disappear ance of slide rules, logarithm tables, and the often error-bound tedium that such tools of the trade demand. Time that used to be spent on the use of logarithm tables and manual square-root extraction can be prof itably turned to earlier studies of calculus or computer programming. Now that the calculator has been accepted into the classroom, we face a computer-software revolution which promises to be considerably more profound. Modern textbooks in the physical sciences routinely assume their readers have access not only to calculators, but often to home or even mainframe computers as well, and the problems teachers discuss and assign students can be more complex and often more realistic than in the days of only pad and pencil computations. As less effort is spent on numerical computation, more can be devoted to conceptual under standing and to applications of the increasingly sophisticated mathe matical methods needed for a real appreciation of recent advances in the discipline."