**[Cr:4, Lc:3, Tt:1, Lb:0]**

- The general and special linear groups.
- Bilinear forms and associated notions.
- Alternating forms and symplectic groups.
- Quadratic forms and orthogonal groups. Wittâ€™s cancellation and extension theorems. Cartan-Dieudonne theorem. Associated simple groups.
- Structure of Clifford algebras and spin groups.
- Hermitian forms and unitary groups.

- Compact real forms of the classical groups, associated Lie algebras and Weyl groups.
- Composition algebras and principle of triality.

- Larry C. Grove, Classical groups and geometric algebra, Graduate Studies in Mathematics, Vol. 39, American Mathematical Society, Providence, RI (2000).
- Nathan Jacobson, Basic algebra (volumes I and II), Dover (2009).
- Serge Lang, Algebra, Graduate Texts in Mathematics (211), Springer-Verlag, New York Inc. (2002).
- Emil Artin, Geometric algebra, Wiley India Pvt. Ltd. (1988).
- Hermann Weyl, Classical groups, Princeton University Press, Princeton (1946).