I will define and discuss the basic notions in symplectic topology (assuming some knowledge of smooth manifolds, forms, singular/DeRham (co)homology, etc). I will also discus the classical invariants such as Gromov-Witten invariants, and their counterparts for Lagrangians. I will try and explain problems/obstructions involved in lifting certain of these invariants to spectra, but also how to sometimes get around these issues. I will try and spend the marjority of the time on basic notions as without these it is impossible to get any insight – this means that some of the more technical and deep theorems will only be discussed at the hand-wavy level (I will however try and formulate these things in terms/relation to known theorems and concepts in algebraic topology).
Breaks will occur.