Consider a set-valued operator mapping points of a real Banach space into convex and weak* closed subsets of the dual space. It is shown that such operators can be investigated via the notion of a form. In particular, continuity, monotonicity, maximal monotonicity, and coerciveness are considered. Moreover, a calculus of forms is derived. Having established the above connections, a probably new sum theorem in nonreflexive Banach spaces is proved, and a Browder-type theorem for forms is given.