- Introduction to Part I
- Chapter I.1: Some higher algebra
- Chapter I.2: Basics of derived algebraic geometry
- Chapter I.3: Quasi-coherent sheaves on prestacks

- Introduction to Part II
- Chapter II.1: Ind-coherent sheaves on schemes
- Chapter II.2: Ind-coherent sheaves as a functor out of the category of correspondences
- Chapter II.3: Interaction of QCoh and IndCoh

- Introduction to Part III
- Chapter III.1: Deformation theory
- Chapter III.2: Ind-schemes and inf-schemes
- Chapter III.3: Ind-coherent sheaves on ind-inf-schemes
- Chapter III.4: An application: crystals

- Introduction to Part IV
- Chapter IV.1: Formal moduli
- Chapter IV.2: Lie algebras and co-commutative co-algebras
- Chapter IV.3: Formal groups and Lie algebras
- Chapter IV.4: Lie algebroids
- Chapter IV.5: Infinitesimal differential geometry

- Introduction to Part V
- Chapter V.1: The (oo,2)-category of correspondences
- Chapter V.2: Extension theorems for the category of correspondences
- Chapter V.3: The (symmetric) monoidal structure on the category of correspondences

- Introduction to Part A
- Chapter A.1: Basics of 2-categories
- Chapter A.2: Straightening and Yoneda for (oo,2)-categories
- Chapter A.3: Adjunctions in (oo,2)-categories