Part I. Motivation: On the Quaternions H. 1. Introduction of Part I. 2. On the Quaternions H. 3. Spectral Analysis on H Under (C2; Ï).

4. 4. On Noncommutative Field H Under (C2; Ï). 5. Free-Probabilistic Data Induced by H. Part II. On the Classical Clifford Algebras. 6.

Introduction of Part II. 7. Classical Clifford Algebras. 8. Free Probability on the Clifford-Group C*-Probability Space (MG; T). 9. Free Probability on Certain Sub-Structures of (MG; T). Part III.

The Clifford Group G and the Semicircular Law. 10. Introduction of Part III. 11. On the Tensor Product C*-Probability C-Spaces (M G Ø A; T Ø '´). 12. Deformed Semicircular Laws on (M GØ A; T Ø '´). 13.

Applications. Part IV. Representations of the Clifford Algebra C. 14. Introduction of Part IV. 15. The Clifford Algebra C Embedded in the CG C*-Algebra M G. 16.

On the R-Banach *-Algebra C. 17. R-Adjointable-Operator-Theoretic Properties on C. 1 8. Discussions.