  We introduce an analog of the Ziegler spectrum for maximal Cohen-Macaulay
modules over a complete Cohen-Macaulay local ring. We define a topology on the
space of isomorphism classes of indecomposable maximal Cohen-Macaulay modules
and investigate the topological structure. We also calculate the
Cantor-Bendixson rank for a ring which is of CM_+-finite representation type.
