Can anyone suggest a good overview/introduction of the Floer machine for a beginner? (Someone pointed out some intriguing connections to surface mapping class groups, which might be enough incentive to dip the toe in (though I suppose "total immersion" might be the only realistic option…)
[Math] Introduction to Floer Theory
dg.differential-geometryfloer-homologygt.geometric-topologysg.symplectic-geometry
Best Answer
Michael Hutchings' lecture notes were precisely for this purpose; posted on his webpage: http://math.berkeley.edu/~hutching/
Lecture Notes on Morse Homology (With an Eye Towards Floer Theory and Pseudoholomorphic Curves)