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- Geometrical Introduction
- Spacetimes
- Local Geodesic Structure
- Geodesics
- Normal, Convex and Simple Neighbourhoods
- The Time
- The Past and the Future
- Causality Condition
- Causally Convex and Strongly Causal Sets
- Global Hyperbolicity
- Perfectly Simple Spacetimes
- Cutting and Pasting’ Spacetimes.
- Physical Predilections
- Locality
- The Maximal Speed and Causality
- Shortcuts
- Time Machines
- A No-Go Theorem for the Artificial Time Machine
- Time Travel Paradoxes
- Quantum Corrections
- WEC-Related Quantum Restrictions
- Primordial Wormhole
- At and Beyond the Horizon