  We generalize the geometry of Santilli's locally anisotropic and
inhomogeneous isospaces to the geometry of vector isobundles provided with
nonlinear and distinguished isoconnections and isometric structures. We
present, apparently for the first time, the isotopies of Lagrange, Finsler and
Kaluza--Klein spaces. We also continue the study of the interior, locally
anisotropic and inhomogeneous gravitation by extending the isoriemannian
space's constructions and presenting a geometric background for the theory of
isofield interactions in generalized isolagrange and isofinsler spaces.
