| Examples and Preliminaries | p. 1 |
| A Jigsaw Puzzle | p. 1 |
| A Geometrical Example | p. 4 |
| The Set of Linear Orders | p. 6 |
| The Set of Partial Orders | p. 7 |
| An Isometric Subgraph of Z2+n | p. 8 |
| Learning Spaces | p. 10 |
| A Genetic Mutations Scheme | p. 11 |
| Notation and Conventions | p. 12 |
| Historical Note and References | p. 17 |
| Problems | p. 19 |
| Basic Concepts | p. 23 |
| Token Systems | p. 23 |
| Axioms for a Medium | p. 24 |
| Preparatory Results | p. 27 |
| Content Families | p. 29 |
| The Effective Set and the Producing Set of a State | p. 30 |
| Orderly and Regular Returns | p. 31 |
| Embeddings, Isomorphisms and Submedia | p. 34 |
| Oriented Media | p. 36 |
| The Root of an Oriented Medium | p. 38 |
| An Infinite Example | p. 39 |
| Projections | p. 40 |
| Problems | p. 45 |
| Media and Well-graded Families | p. 49 |
| Wellgradedness | p. 49 |
| The Grading Collection | p. 52 |
| Wellgradedness and Media | p. 54 |
| Cluster Partitions and Media | p. 57 |
| An Application to Clustered Linear Orders | p. 62 |
| A General Procedure | p. 68 |
| Problems | p. 68 |
| Closed Media and U-Closed Families | p. 73 |
| Closed Media | p. 73 |
| Learning Spaces and Closed Media | p. 78 |
| Complete Media | p. 80 |
| Summarizing a Closed Medium | p. 83 |
| U-Closed Families and their Bases | p. 86 |
| Projection of a Closed Medium | p. 94 |
| Problems | p. 98 |
| Well-Graded Families of Relations | p. 101 |
| Preparatory Material | p. 102 |
| Wellgradedness and the Fringes | p. 103 |
| Partial Orders | p. 106 |
| Biorders and Interval Orders | p. 107 |
| Semiorders | p. 110 |
| Almost Connected Orders | p. 114 |
| Problems | p. 119 |
| Mediatic Graphs | p. 123 |
| The Graph of a Medium | p. 123 |
| Media Inducing Graphs | p. 125 |
| Paired Isomorphisms of Media and Graphs | p. 130 |
| From Mediatic Graphs to Media | p. 132 |
| Problems | p. 136 |
| Media and Partial Cubes | p. 139 |
| Partial Cubes and Mediatic Graphs | p. 139 |
| Characterizing Partial Cubes | p. 142 |
| Semicubes of Media | p. 149 |
| Projections of Partial Cubes | p. 151 |
| Uniqueness of Media Representations | p. 154 |
| The Isometric Dimension of a Partial Cube | p. 158 |
| Problems | p. 159 |
| Media and Integer Lattices | p. 161 |
| Integer Lattices | p. 161 |
| Defining Lattice Dimension | p. 162 |
| Lattice Dimension of Finite Partial Cubes | p. 167 |
| Lattice Dimension of Infinite Partial Cubes | p. 171 |
| Oriented Media | p. 172 |
| Problems | p. 174 |
| Hyperplane arrangements and their media | p. 177 |
| Hyperplane Arrangements and Their Media | p. 177 |
| The Lattice Dimension of an Arrangement | p. 184 |
| Labeled Interval Orders | p. 186 |
| Weak Orders and Cubical Complexes | p. 188 |
| Problems | p. 196 |
| Algorithms | p. 199 |
| Comparison of Size Parameters | p. 199 |
| Input Representation | p. 202 |
| Finding Concise Messages | p. 211 |
| Recognizing Media and Partial Cubes | p. 217 |
| Recognizing Closed Media | p. 218 |
| Black Box Media | p. 222 |
| Problems | p. 227 |
| Visualization of Media | p. 229 |
| Lattice Dimension | p. 230 |
| Drawing High-Dimensional Lattice Graphs | p. 231 |
| Region Graphs of Line Arrangements | p. 234 |
| Pseudoline Arrangements | p. 238 |
| Finding Zonotopal Tilings | p. 246 |
| Learning Spaces | p. 252 |
| Problems | p. 260 |
| Random Walks on Media | p. 263 |
| On Regular Markov Chains | p. 265 |
| Discrete and Continuous Stochastic Processes | p. 271 |
| Continuous Random Walks on a Medium | p. 273 |
| Asymptotic Probabilities | p. 279 |
| Random Walks and Hyperplane Arrangements | p. 280 |
| Problems | p. 282 |
| Applications | p. 285 |
| Building a Learning Space | p. 285 |
| The Entailment Relation | p. 291 |
| Assessing Knowledge in a Learning Space | p. 293 |
| The Stochastic Analysis of Opinion Polls | p. 297 |
| Concluding Remarks | p. 302 |
| Problems | p. 303 |
| Appendix: A Catalog of Small Mediatic Graphs | p. 305 |
| Glossary | p. 309 |
| Bibliography | p. 311 |
| Index | p. 321 |
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