Professor Susskind begins the lecture with a review of Kruskal coordinates, and how they apply to the study of black holes. He then moves on to develop a coordinate system which allows the depiction of all of spacetime on a finite blackboard. This results in a Penrose diagram for flat spacetime. The Penrose diagram for black holes leads to an understanding of wormholes, also known as Einstein-Rosen bridges.

Professor Susskind then describes the process of black hole formation through the simplest possible mechanism: an infalling sphere of radiation. This process is studied by marrying a Penrose diagram for the flat spacetime inside the sphere, with a Penrose diagram for the black hole under formation outside the sphere of radiation. The boundary between the two diagrams is the radiation sphere itself, and this approach demonstrates how the black hole horizon develops and begins to expand even before the black hole itself forms.

- Kruskal–Szekeres coordinates
- Penrose diagrams
- Wormholes
- Formation of a black hole
- Newton's shell theorem