  We study the Ricci flow for initial metrics with positive isotropic curvature
(strictly PIC for short).
  In the first part of this paper, we prove new curvature pinching estimates
which ensure that blow-up limits are uniformly PIC in all dimensions. Moreover,
in dimension $n \geq 12$, we show that blow-up limits are weakly PIC2. This can
be viewed as a higher-dimensional version of the fundamental Hamilton-Ivey
pinching estimate in dimension $3$.
  In the second part, we develop a theory of ancient solutions which have
bounded curvature; are $\kappa$-noncollapsed; are weakly PIC2; and are
uniformly PIC. This is an extension of Perelman's work; the additional
ingredients needed in the higher dimensional setting are the differential
Harnack inequality for solutions to the Ricci flow satisfying the PIC2
condition, and a rigidity result due to Brendle-Huisken-Sinestrari for ancient
solutions that are uniformly PIC1.
  In the third part of this paper, we prove a Canonical Neighborhood Theorem
for the Ricci flow with initial data with positive isotropic curvature, which
holds in dimension $n \geq 12$. This relies on the curvature pinching estimates
together with the structure theory for ancient solutions. This allows us to
adapt Perelman's surgery procedure to this situation. As a corollary, we obtain
a topological classification of all compact manifolds with positive isotropic
curvature of dimension $n \geq 12$ which do not contain non-trivial
incompressible $(n-1)$-dimensional space forms.
