  In this largely expository paper we give a self-contained treatment of the
Dirac operator. Emphasizing the algebraic point of view we first sketch the
necessary prerequisites from Clifford algebras and their representations and
then define (and characterize) spin structures and the corresponding Spin-Dirac
operator purely in the spirit of irreducible representations. We also prove its
equivalence with the usual approach via principal bundles. We conclude with
other geometric Dirac operators and their properties using the afore-mentioned
setting.
