  In these survey lectures, we investigate the geometric and analytic
properties of transverse Dirac operators. In particular, we define a transverse
Dirac operator associated to a distribution that is essentially self-adjoint
(Prokhorenkov-R result). We describe the Habib-R Theorem showing that the
invariance of the spectrum of a basic Dirac operator on a Riemannian foliation.
The Bruening-Kamber-R theorems give Atiyah-Singer type formulas for the
equivariant index of transversally elliptic operators on G-manifolds and the
index of basic Dirac operators on Riemannian foliations. These notes contain
exercises at the end of each subsection and are meant to be accessible to
graduate students.
