  This paper is the third of a series of three, and it is the continuation of
math-ph/0412074 and math-ph/0412075. After reviewing the conformal spacetime
structure, conformal maps are described in Minkowski spacetime as the twisted
adjoint representation of the group Spin_+(2,4), acting on paravectors.
Twistors are then presented via the paravector model of Clifford algebras and
related to conformal maps in the Clifford algebra over the lorentzian R{4,1}$
spacetime. We construct twistors in Minkowski spacetime as algebraic spinors
associated with the Dirac-Clifford algebra Cl(1,3)(C) using one lower spacetime
dimension than standard Clifford algebra formulations, since for this purpose
the Clifford algebra over R{4,1} is also used to describe conformal maps,
instead of R{2,4}. Although some papers have already described twistors using
the algebra Cl(1,3)(C), isomorphic to Cl(4,1), the present formulation sheds
some new light on the use of the paravector model and generalizations.
