  In this paper, we set up two surgery theories and two kinds of Whitehead
torsion for foliations. First, we construct a bounded surgery theory and
bounded Whitehead torsion for foliations, which correspond to the Connes'
foliation algebra in the K-theory of operator algebras, in the sense that there
is an analogy between surgery theory and index theory, and a Novikov Conjecture
for bounded surgery on foliations in analogy with the foliated Novikov
conjecture of P.Baum and A.Connes in operator theory. This surgery theory
classifies the leaves topologically. Secondly, we construct a bounded geometry
surgery for foliations, which is a generalization of blocked surgery, and a
bounded geometry Whitehead torsion. The classifications in this surgery theory
include the specification of the Riemannian metrics of the leaves up to
quasi=isometry. We state Borel conjectures for foliations, which solves a
problem posed by S.Weinberger \cite{Wein}, and verify these in some cases of
geometrical interest.
