Calabi-Yau manifolds play the most fundamental role in the development of classification theory of higher dimensional algebraic geometry as well in string theory in the last 2 decades. There are essentially two types of research results in such studies. One is based on example study (especially those in physics and in mathematical study on mirror symmetry) and another one is from the purely theoretic point of view.
The plan of this course is to address on the pure theoretic results that works for general Calabi-Yau manifolds or singular Calabi-Yau varieties. Especially, we shall focus on structural theorem based on holonomy, unobstructed deformations, small resolutions and smoothings (transitions), stability and structure of Kaehler cones, Mori contractions, K-equivalence, elliptic genera, Weil-Petersson geometry on moduli, symplectic surgeries etc.