This summer school (July 2023) was a series of eight mini-courses. My notes are incomplete in places. If you find any errors, please let me know. I was learning much of this material for the first time at the time of writing them. Find more info on the Princeton Summer School on the website. 

Introduction to Knot Theory and Knot Homologies

Introduction to Heegaard Floer Homology

Surfaces in 4-manifolds

Moduli Spaces of Pseudo-holomorphic Curves

An Introduction to the Volume Conjecture

Lattice Homology and Bordered Floer Homology

Immersed Curves and Invariants of Knots and 3-manifolds

Introduction to Symplectic Geometry