Part I. The algebraic theory of spinors.
(i) Clifford algebras: structure and representation theory.
(ii) Spin groups and spinor representations.
Part II. K-Theory and characteristic classes.
(i) -theory and -theory.
(ii) Classifying spaces and characteristic classes.
(iii) Bott Periodicity and the relationship to Clifford algebras.
Part III. Spin-manifolds and Spin-manifolds.
(i) Spin-manifolds - definitions and examples.
(ii) Spin-manifolds - definitions and examples.
Part IV. Spinor bundles, connections and Dirac operators.
(i) Clifford and Spinor bundles.
(ii) The Levi-Civita connection on spinors.
(iii) Construction of the Dirac operators.
Part V. The Atiyah-Singer Index Theorem.
(i) The index theorem.
(ii) The index theorem for families.
(iii) The C-index theorem.
Part VI. Applications to geometry and topology.