Completely positive linear mappings between C*-algebras were originally
developed in the 1950's as a special case of positive linear operators
between matrix algebras. Within the last two decades, mathematical
physicists have determined that completely positive maps play a crucial
role in quantum information theory as structures which model information
transfer between quantum systems. This talk will serve as an introduction
to two classes of completely positive maps: the Schur maps which arise
from the Schur matrix product and maps which are equal to their adjoint.
After focusing on results concerning the geometry of these two sets of
CP maps, we introduce a general framework that unifies certain classes
of CP maps in terms of C*-subalgebras of Mn.