| Introduction | p. 1 |
| The Hahn-Banach-Lagrange theorem and some consequences | |
| The Hahn-Banach-Lagrange theorem | p. 15 |
| Applications to functional analysis | p. 23 |
| A minimax theorem | p. 24 |
| The dual and bidual of a normed space | p. 25 |
| Excess, duality gap, and minimax criteria for weak compactness | p. 28 |
| Sharp Lagrange multiplier and KKT results | p. 32 |
| Fenchel duality | |
| A sharp version of the Fenchel Duality theorem | p. 41 |
| Fenchel duality with respect to a bilinear form - locally convex spaces | p. 44 |
| Some properties of 1/2 . 2 | p. 49 |
| The conjugate of a sum in the locally convex case | p. 51 |
| Fenchel duality vs the conjugate of a sum | p. 54 |
| The restricted biconjugate and Fenchel-Moreau points | p. 58 |
| Surrounding sets and the dom lemma | p. 60 |
| The ⊖-theorem | p. 62 |
| The Attouch-Brezis theorem | p. 65 |
| A bivariate Attouch-Brezis theorem | p. 67 |
| Multifunctions, SSD spaces, monotonicity and Fitzpatrick functions | |
| Multifunctions, monotonicity and maximality | p. 71 |
| Subdifferentials are maximally monotone | p. 74 |
| SSD spaces, q-positive sets and BC-functions | p. 79 |
| Maximally q-positive sets in SSD spaces | p. 86 |
| SSDB spaces | p. 88 |
| The SSD space E × E* | p. 93 |
| Fitzpatrick functions and fitzpatrifications | p. 99 |
| The maximal monotonicity of a sum | p. 103 |
| Monotone multifunctions on general Banach spaces | |
| Monotone multifunctions with bounded range | p. 107 |
| A general local boundedness theorem | p. 108 |
| The six set theorem and the nine set theorem | p. 108 |
| D(Sϕ) and various hulls | p. 111 |
| Monotone multifunctions on reflexive Banach spaces | |
| Criteria for maximality, and Rockafellar's surjectivity theorem | p. 117 |
| Surjectivity and an abstract Hammerstein theorem | p. 123 |
| The Brezis-Haraux condition | p. 125 |
| Bootstrapping the sum theorem | p. 128 |
| The > six set and the > nine set theorems for pairs of multifunctions | p. 130 |
| The Brezis-Crandall-Pazy condition | p. 132 |
| Special maximally monotone multifunctions | |
| The norm-dual of the space E × E* and <$>-functions | p. 139 |
| Subclasses of the maximally monotone multifunctions | p. 147 |
| First application of Theorem 35.8: type (D) implies type (FP) | p. 153 |
| Tclb(E**), Tclbn(B*) and type (ED) | p. 154 |
| Second application of Theorem 35.8: type (ED) implies type (FPV) | p. 157 |
| Final applications of Theorem 35.8: type (ED) implies strong | p. 158 |
| Strong maximality and coercivity | p. 159 |
| Type (ED) implies type (ANA) and type (BR) | p. 161 |
| The closure of the range | p. 167 |
| The sum problem and the closure of the domain | p. 170 |
| The biconjugate of a maximum and Tclb(E**) | p. 172 |
| Maximally monotone multifunctions with convex graph | p. 180 |
| Possibly discontinuous positive linear operators | p. 183 |
| Subtler properties of subdifferentials | p. 188 |
| Saddle functions and type (ED) | p. 192 |
| The sum problem for general Banach spaces | |
| Introductory comments | p. 197 |
| Voisei's theorem | p. 197 |
| Sums with normality maps | p. 198 |
| A theorem of Verona-Verona | p. 199 |
| Open problems | p. 203 |
| Glossary of classes of multifunctions | p. 205 |
| A selection of results | p. 207 |
| Referencess | p. 233 |
| Subject index | p. 239 |
| Symbol index | p. 243 |
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