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Bringing geometric algebra to the mainstream of physics pedagogy, this book presents geometric algebra as a discipline within mathematical physics and shows how geometric algebra can be applied to numerous fundamental problems in physics, especially in experimental situations. It introduces the essential features of postulates and their underlying framework; bivectors, multivectors, and their operators; spinor and Lorentz rotations; and Clifford algebra, extending some of these topics into three dimensions. Well-known for their research in general relativity, the authors cover Maxwell's equations, electromagnetic waves' states of polarization, the Dirac equation, wave functions, fiber bundles, and the quantization of gravity.