  As a continuation of the paper [20] on standard $f$-divergences, we make a
systematic study of maximal $f$-divergences in general von Neumann algebras.
For maximal $f$-divergences, apart from their definition based on Haagerup's
$L^1$-space, we present the general integral expression and the variational
expression in terms of reverse tests. From these definition and expressions we
prove important properties of maximal $f$-divergences, for instance, the
monotonicity inequality, the joint convexity, the lower semicontinuity, and the
martingale convergence. The inequality between the standard and the maximal
$f$-divergences is also given.
