Principal results

	Exhaustive classification of nonlinear generalizations of the Dirac equation of an electron invariant under the Poincare group P(1,3) and its extensions, the extended Poincare Sim(1,3) and conformal C(1,3) groups. The classes of thus obtained invariant equations contain as particular cases the well-known Ivanenko, Heisenberg and Gursey nonlinear spinor models (see the items A-1,2; B-1,4,6 of the Publication list )
	Group classification of nonlinear generalizations of the Levi-Leblond equation (a non-relativistic analog of the Dirac equation of an electron) invariant under the Galilei group G(1,3) and its extensions (see the items A-1,2; B-2,11 of the Publication list )
	Complete description of P(1,3), Sim(1,3), C(1,3) inequivalent ansatzes for the Dirac field invariant under the connected 1-, 2- and 3-parameter subgroups of the Poincare, extended Poincare and conformal groups. Construction of Galilei-invariant ansatzes for the non-relativistic spinor field invariant under the connected 1-, 2- a nd 3-parameter subgroups of the Galilei group (see the items A-1,2; B-4,6,11 of the Publication list ).
	Symmetry reduction of the nonlinear Dirac, Levi-Leblond and SU(2) Yang-Mills equations and construction of broad multi-parameter families of their classical solutions (see the items A-1,2; B-1,2,4,6,8,9,11,21,24,26 of the Publication list ).