  In this paper we present some approaches to classification of almost complex
structures and to construction of local or formal pseudoholomorphic mapping
from one almost complex manifold to another. The corresponding criteria are
given in terms of Nijenhuis tensors and their generalizations.
  We deal with the prolongations of the Cauchy-Riemann equation in 1-jets of
the mapping from one almost complex manifold to another. We give a criterion of
the prolongation existence of k-th pseudoholomorphic jets to the (k+1)-th ones.
As a consequence basing on the Kuranishi's approach we obtain formal normal
forms of almost complex structures. As another consequence we get the formal
part of Newlander-Nirenberg's theorem on integrability.
  We also introduce the notion and study the properties of the linear Nijenhuis
tensor, which we apply to almost complex structures of general position. Two
applications are exhibited: a classification of four-dimensional almost complex
structures in terms of distributions and a characterization of the new class of
structures which we call Lie almost complex structures.
