I am interested in learning Mirror Symmetry, both from the SYZ and Homological point of view. I am taking a reading course in Mirror Symmetry, which will focus on the SYZ side. I know basic Complex geometry, Kahler manifolds, Symplectic manifolds in the geometric side and also reading some material for my course on SYZ conjecture. My major concern is Homological side, about which I have little knowledge.
I am seeking a list of good references for SYZ conjecture, Homological Mirror Symmetry, physics of the theory, modern developments and on its relation to other areas of mathematics and some original papers (preferably in Chronological order).
What are your views about the Claire Voisin's book on Mirror Symmetry. And what is the present status of research in Mirror Symmetry, I mean what type of problems are people working on.