  We study the maximal rigid subcategories in $2-$CY triangulated categories
and their endomorphism algebras. Cluster tilting subcategories are obviously
maximal rigid; we prove that the converse is true if the $2-$CY triangulated
categories admit a cluster tilting subcategory. As a generalization of a result
of [KR], we prove that any maximal rigid subcategory is Gorenstein with
Gorenstein dimension at most 1. Similar as cluster tilting subcategory, one can
mutate maximal rigid subcategories at any indecomposable object. If two maximal
rigid objects are reachable via mutations, then their endomorphism algebras
have the same representation type.
