Focusing on the theory of monotone multifunctions on a Banach space, this work looks at the big convexification of a multi-function, convex functions associated with a multifunction, minimax theorems as a tool in functional analysis, and convex analysis. Topics include: results on the existence of continuous linear functionals; the conjugates, biconjugates and subdifferentials of convex lower semicontinuous functions; Fenchel duality; positive linear operators from a Banach space into its dual; the sum of maximal monotone operators; and a list of open problems. The reader is expected to know basic functional analysis and calculus of variations, including the Bahn-Banach theorem, Banach-Alaoglu theorem, and Ekeland’s variational principle.