This is the third of four lectures given about "Quadratic Forms and Automorphic Forms" at the 2009 Arizona Winter School, to an audience of interested graduate students. Detailed notes supporting these lectures are available at: arxiv.org/abs/1105.5759
This lecture introduces quaternion algebras and explains how they are related to the Clifford algebra of a quadratic form. The Clifford algebra is used to construct the "spin" double cover of the orthogonal group, which gives rise to the useful (local) notion of spinor equivalence.
