We establish the basic analytic properties of mappings of finite distortion between proper Ahlfors regular metric measure spaces that support a
(
1
,
1
)
(1,1)
-Poincaré inequality. As applications, we prove that under certain integrability assumption for the distortion function, the branch set of a mapping of finite distortion between generalized
n
n
-manifolds of type
A
A
has zero Hausdorff
n
n
-measure.