Contents -- Introduction -- 1. A Taste of Clifford Algebra in Euclidean 3-Space -- 1.1 Reflections, Rotations, and Quaternions in E[sup(3)] via Clifford Algebra -- 1.2 'The 4π Periodicity of the Rotation Operator -- 1.3* The Spinning Top (One Point Fixed)-Without Euler Angles -- 2. A Sample of Clifford Algebra in Minkowski 4-Space -- 2.1 A Small Dose of Special Relativity -- 2.2 Mass, Energy, and Momentum -- 3. Clifford Algebra for Flat n-Dimensional Spaces -- 3.1 Clifford Numbers in n-Dimensional Euclidean or Pseudo-Euclidean Spaces -- 3.2 Dirac Matrices in Real Euclidean or Pseudo-Euclidean Spaces -- 3.3 The Metric Tensor and the Scalar Product for 1-Vectors -- 3.4 The Exterior Product for p-Vectors and the Scalar Product for Clifford Numbers -- 4. Curved Spaces Embedded in Higher Dimensional Flat Spaces -- 4.0 Why you may wish to skip Chapter 4 -- 4.1 Gaussian Curvature and Parallel Transport on Two-Dimensional Surfaces in E[sup(3)] -- 4.2 The Operator [omitted][sub(v)] on an m-Dimensional Surface Embedded in an n-Dimensional Flat Space -- 4.3 Parallel Transport on an m-Dimensional Surface Embedded in an n-Dimensional Flat Space -- 5. The Use of Fock-Ivanenko 2-Vectors to obtain the Schwarzschild Metric -- 5.1 The Operator [omitted][sub(α)] and Dirac Matrices in Curved Spaces -- 5.2 Connection Coefficients and Fock-Ivanenko 2-Vectors -- 5.3 The Riemann Curvature Tensor and its Symmetries -- 5.4 The Use of Fock-Ivanenko 2-Vectors to Compute Curvature 2-Forms -- 5.5* The Interpretation of Curvature 2-Forms as Infinitesimal Rotation Operators -- 6*. The Schwarzschild Metric via Fock-Ivanenko 2-Vectors -- 6.1 The Use of Fock-Ivanenko 2-Vectors to Determine the Schwarzschild Metric -- 6.2 The Precession of Perihelion for Mercury -- 7. Two Differential Operators.

7.1 The Exterior Derivative d and the Codifferential Operator δ Related to the Operator [omitted] = γ[sup(J)][omitted][sub(J)] -- 7.2 Maxwell's Equations in Flat Space -- 7.3* Is Gravity a Yang-Mills Field? -- 7.4* The Migma Chamber of Bogdan Maglich -- 7.5* The Generalized Stake's Theorem -- 8.* Dirac's Equation for the Electron -- 8.1 Currents and Dipoles in Curved Space Resulting from Dirac's Equation for the Electron -- 8.2 Clifford Solutions for the Free Electron in Flat Space -- 8.3 A Canonical Form for Solutions to Dirac's Equation in Flat Space -- 8.4 Spherical Harmonic Clifford Functions -- 8.5 Clifford Solutions of Dirac's Equation for Hydrogen-like Atoms -- 9. The Kerr Metric by an Elementary Brute Force Method -- 9.1 The Kerr Metric -- 10.* Petrov's Canonical Forms for the Weyl Tensor and Another Approach to the Kerr Metric -- 10.1 Petrov's Canonical Forms for the Weyl Tensor -- 10.2 Principal Null Directions -- 10.3 The Kerr Metric Revisited via its Petrov Matrix -- 11.* Matrix Representations and Classifications of Clifford Algebras -- 11.1 Matrix Representations of Clifford Algebras -- 11.2 The Classification of all Real Finite Dimensional Clifford Algebras -- 11.3 The Classification of all c-Unitary Groups -- Appendix: -- A.1 The Product Decomposition of Restricted Lorentz Operators and Related Operators -- A.2 The Exponential Representation of Restricted Lorentz Operators -- A.3 The Bianchi Identity -- Bibliography -- Index -- A -- B -- C -- D -- E -- F -- G -- H -- I -- J -- K -- L -- M -- N -- O -- P -- Q -- R -- S -- T -- U -- V -- W -- Y -- Z.