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In this paper, we compute the inertia groups of $(n-1)$-connected, smooth,closed, oriented $2n$-manifolds where $n \geq 3$. As a consequence, we completethe diffeomorphism classification of such manifolds, finishing a programinitiated by Wall sixty years ago, with the exception of the $126$-dimensionalcase of the Kervaire invariant one problem.  In particular, we find that the inertia group always vanishes for $n \neq4,8,9$ -- for $n \gg 0$, this was known by the work of several previousauthors, including Wall, Stolz, and Burklund and Hahn with the first namedauthor. When $n = 4,8,9$, we apply Kreck's modified surgery and a special caseof Crowley's $Q$-form conjecture, proven by Nagy, to compute the inertia groupsof these manifolds. In the cases $n=4,8$, our results recover unpublished workof Crowley--Nagy and Crowley--Olbermann.  In contrast, we show that the homotopy and concordance inertia groups of$(n-1)$-connected, smooth, closed, oriented $2n$-manifolds with $n \geq 3$always vanish.

Inertia groups of $(n-1)$-connected $2n$-manifolds