Geometric Algebra (GA) is a powerful mathematical language for expressing physical ideas. It unifies many diverse mathematical formalisms and aids physical intuition. In our various publications and lectures you will find many examples of the insights that geometric algebra brings to problems in physics and engineering.
The most up-to-date introduction to Geometric Algebra is provided in the series of lectures given as part of the 2015 introductory course on GA.
The paper “Imaginary Numbers are not Real” provides a brief, but readable introduction to geometric algebra. The most complete introduction to the subject is contained in the book “Geometric Algebra for Physicists” (CUP 2003). For a number of years we ran a lecture course on geometric algebra for final year physics undergraduates in Cambridge University. The material for the course is provided here.
The publications page illustrates our group’s research interests. These include applications of geometric algebra to classical mechanics, classical and quantum electrodynamics, gravitation, Dirac theory, multiparticle quantum mechanics and quantum information, spinors and twistors, computer graphics and computational geometry, robotics, and other applications in engineering.
There is a wikipedia entry on geometric algebra, which is pretty detailed and provides a detailed list of additional material.