We will explain one side of the equality in the Atiyah-Singer index theorem. It is the index of a Dirac-type operator on a vector bundle $$E$$. To accomplish this we introduce in order, partial differential operators on bundles, their symbols, ellipticity, the index of a Fredholm operator, Dirac-type operators. Concrete examples of these concepts will be shown. This is expository and no proofs will be shown, although some technique will be demonstrated.