  This paper is the second one of a series of three and it is the continuation
of math-ph/0412074. We review some properties of the algebraic spinors in
Cl(3,0) and Cl(0,3) and how Weyl, Pauli and Dirac spinors are constructed in
Cl(3,0) (and Cl(0,3) in the case of Weyl spinors. A plane wave solution for the
Dirac equation is obtained, and the Dirac equation is written in terms of Weyl
spinors, and alternatively, in terms of Pauli spinors. Finally the covariant
and contravariant undotted spinors in Cl(0,3), isomorphic to two copies of the
quaternion algebra (H), are constructed. We prove that there exists an
application that maps the even subalgebra Cl+(0,3) of Cl(0,3), viewed as a
right H-module, onto Cl+(0,3), but now viewed as a left H-module.
