Spectral algebraic geometry

Introduction
I Fundamentals of Spectral Algebraic Geometry
	Schemes and Deligne-Mumford Stacks
	Quasi-Coherent Sheaves
	Spectral Algebraic Spaces
II Proper Morphisms
	Morphisms of Finite Presentation
	Proper Morphisms in Spectral Algebraic Geometry
	Grothendieck Duality
	Nilpotent, Local, and Complete Modules
	Formal Spectral Algebraic Geometry
III Tannaka Reconstruction and Quasi-Coherent Stacks
	Tannaka Duality
	Quasi-Coherent Stacks
	Smooth and Proper Linear -Categories
IV Formal Moduli Problems
	Deformation Theories: Axiomatic Approach
	Moduli Problems for Commutative Algebras
	Moduli Problems for Associative Algebras
	Moduli Problems for En-Algebras
	Examples of Formal Moduli Problems
V Representability Theorems
	Deformation Theory and the Cotangent Complex
	Artin's Representability Theorem
	Applications of Artin Representability
VI Structured Spaces
	Fractured -Topoi
	Structure Sheaves
	Scheme Theory
VII Variants of Spectral Algebraic Geometry
	Derived Differential Topology
	Derived Complex Analytic Geometry
	Derived Algebraic Geometry
VIII Higher Algebraic Stacks
	Algebraic Stacks in Derived Algebraic Geometry
	Artin Representability
	Coaffine Stacks
	Generalized Algebraic Gerbes
IX Rational and p-adic Homotopy Theory
	Rational Homotopy Theory
	p-adic Homotopy Theory
	Unstable Riemann-Hilbert Correspondence
X Appendix
	Coherent -Topoi
	Grothendieck Topologies in Commutative Algebra
	Prestable -Categories
	Descent for Modules and Linear -Categories
	Profinite Homotopy Theory