  Some recent work in Frechet geometry is briefly reviewed. In particular an
earlier result on the structure of second tangent bundles in the finite
dimensional case was extended to infinite dimensional Banach manifolds and
Frechet manifolds that could be represented as projective limits of Banach
manifolds. This led to further results concerning the characterization of
second tangent bundles and differential equations in the more general Frechet
structure needed for applications. A summary is given of recent results on
hypercyclicity of operators on Frechet spaces.
