  We introduce Gorenstein silting modules (resp. complexes), and give the
relation with the usual silting modules (resp. complexes). We show that
Gorenstein silting modules are the module-theoretic counterpart of 2-term
Gorenstein silting complexes; and partial Gorenstein silting modules are in
bijection with \tau_{G}-rigid modules for finite dimensional algebras of finite
CM-type. We also give the relation between 2-term Gorenstein silting complexes,
t-structures and torsion pair in module categories; and generalise the
classical Brenner-Butler theorem to this setting; and characterise the global
dimension of endomorphism algebras of 2-term Gorenstein silting complexes over
an algebra A by terms of the Gorenstein global dimension of A.
