This two-volume set presents combinatorial functional equations using an algebraic approach, and illustrates their applications in combinatorial maps, graphs, networks, etc. The first volume mainly presents basic concepts and the theoretical background. Differential (ordinary and partial) equations and relevant topics are discussed in detail.

• Preface 6
• Contents 10
• Introduction 14
• 1. Preliminaries 22
• 2. Meson functional 42
• 3. Function equations of one variable 62
• 4. Equations of function with several variables 98
• 5. Difference equations 126
• 6. Ordinary differential equations 158
• 7. Partial differential equations 190
• 8. Tree equations 236
• 9. Near-tree equations first part 264
• 10. Near-tree equations second part 278
• Bibliography 298
• Index 302