While focusing primarily on moduli spaces of closed curves, we hope to also discuss several extensions involving moduli spaces of curves with extra structures (eg twisted versions, the version relative a normal crossing divisor and Real versions). Time permitting, we might mention some open versions (eg curves with boundary on a Lagrangian or SFT).

• Part 1: Topological preliminaries: Relative fundamental classes and their properties;
• Thinly compactified manifolds and fundamental classes; thinly compactified families and relative fundamental classes
• Compatibility of relative fundamental classes of thin compactification with other VFC definitions: (a) using pseudocycles, (b) using "cut-down" moduli spaces and (c) using Pardon's implicit atlases
• Part 2: Moduli spaces of (perturbed) pseudo-holomorphic curves: basic properties
• Preliminaries: Basic properties of holo curves; simple curves and multiple covers; Cauchy-Riemann type operators
• Compactifications: (a) moduli spaces of stable maps with Gromov topology and (b) spaces of pseudo-holomorphic cycles with geometric convergence and (c) the relation between them
• Overview of the Deligne-Mumford space; Teichmuller slices and Kodaira-Spencer deformation theory; global regular covers and the universal curve
• Deformation theory: linearizations and transversality, Ruan-Tian perturbations, orientability and orientations
• Gromov-Witten invariants;
• Other examples of moduli spaces: (a) prescribed order of contact to a divisor and relative moduli space compactifications; (b) moduli spaces of Real maps. If time permits: relation to SFT compactification and moduli space of curves with boundary on Lagrangian
• Part 3: The proof of the Gopakumar-Vafa conjecture and the structure of Gromov-Witten invariants of symplectic 6-dimensional symplectic manifolds
• The structure of the space of simple pseudo-holomorphic curves
• Decomposing the moduli space into clusters of curves
• The cluster isotopy/wall-crossing theorem and local Kuranishi models at wall crossings
• Elementary clusters and their contribution to Gromov-Witten invariants; super-rigid curves and their obstruction bundle;
• Outline of Bryan-Pandharipande calculation: virtual contributions define a TQFT and the target splitting formula
• Part 4: Splitting/Gluing Formulas
• Preliminaries: weighed Sobolev norms and Cauchy-Riemann type operators; short exact sequences of Fredholm operators and the Snake Lemma; the evaluation SES and the normalization SES
• Linear gluing for families of Cauchy-Riemann type operators; application: the obstruction bundle for super-rigid curves
• Splitting/gluing the domains and the standard gluing theorem; application: the contribution of super-rigid curves
• Splitting/gluing the targets and the TQFT splitting axiom