1. Introduction: Some Brief Historical and Philosophical Remarks.- 2. A Brief Introduction to Constructive Type Theory.- 3. Basic Notions for Dialogical Logic.- 4. Advanced Dialogues: Play Level.- 5. Advanced Dialogues: Strategy Level.- 6. Local Reasons and Dialogues for Immanent Reasoning.- 7. The Dialogical Roots of Equality: Dialogues for Immanent Reasoning.- 8. The Remarkable Case of the Axiom of Choice.- 9. From Dialogical Strategies To CTT-Demonstrations...