  Our goal in this paper is to compute the integral free loop space homology of
$(n-1)$-connected $2n$-manifolds $M$, $n\geq 2$. We do this when $n\neq 2,4,8$,
or when $n\neq 2$ and $\tilde H^*(M)$ has trivial cup product squares, though
the techniques used here should extend to a much wider range of manifolds. We
also give partial information concerning the action of the Batalin-Vilkovisky
operator.
