  The purpose of this survey is to explain an approach to the Atiyah-Floer
conjecture via a new instanton Floer homology with Lagrangian boundary
conditions. This is a joint project with Dietmar Salamon. This paper also
provides a rough guide to the analysis of anti-self-dual instantons with
Lagrangian boundary conditions (in earlier papers), which is the crucial
ingredient of our approach.
