CR manifolds of finite and infinite Bloom-Graham type: a comparison

For manifolds of finite Bloom-Graham type there are two well-known results: the theorem of Bloom and Graham about the equivalence of two definitions of type and the criterion of finite dimensionality for the Lie algebra of infinitesimal holomorphic automorphisms. Analogous results for infinite type manifolds were absent. We will fill this gaps and compare manifolds of finite and infinite type in their various aspects (automorphisms, model surfaces, invariants, the structure of sets of fixed type).