  We outline an unified approach to geometrization of Lagrange mechanics,
Finsler geometry and geometric methods of constructing exact solutions with
generic off-diagonal terms and nonholonomic variables in gravity theories. Such
geometries with induced almost symplectic structure are modelled on
nonholonomic manifolds provided with nonintegrable distributions defining
nonlinear connections. We introduce the concept of Lagrange-Fedosov spaces and
Fedosov nonholonomic manifolds provided with almost symplectic connection
adapted to the nonlinear connection structure.
  We investigate the main properties of generalized Fedosov nonholonomic
manifolds and analyze exact solutions defining almost symplectic Einstein
spaces.
