Minimax and Monotonicity Focussing on the theory (both classical and recent) of monotone multifunctions on a (possibly nonreflexive) Banach space this book looks at the big convexification of a multifunction; convex functions associated with a multifunction; minimax theorems as a tool in functional analysis and convex analysis. It includes new results on the existence of continuous linear functionals; the conjugates biconjugates and subdifferentials of convex lower semicontinuous functions Fenchel duality; (possibly unbounded) 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 Ekelands variational principle