  In this paper, we describe the space of adapted connections on a metric
contact manifold through the space of their torsion tensors. The torsion tensor
is an element of the space of TM-valued two-forms, which splits into various
subspaces. We study the parts of the torsion tensor according to this splitting
to completely describe the space of adapted connections. We use this
description to obtain characterizations of the generalized Tanaka-Webster
connection and to describe the Dirac operators of adapted connections.
