  We study jets of germs of holomorphic maps between two strongly pseudoconvex
domains under the condition that the image of one domain is contained into the
other and a given boundary point is (non-tangentially) mapped to a given
boundary point. We completely characterize the (non-tangential) 1-jets.
Moreover we give algebraic inequalities (in terms of Chern-Moser normal forms
up to a certain low order) for the admissible germs with a given 1-jet. Also,
we prove a rigidity result which says that there exists a germ tangent to the
Identity (in some local charts) if and only if the two domains are tangent up
to weighted order five.
