The aim of this school is to introduce the younger researchers and graduate students to the modern trends of the theory of singularities, including both algebraic and geometric aspects, and both classical approaches and the newest ones, related to derived categories, noncommutative geometry, representation theory, tropical geometry, etc. In particular, introductory courses in these areas will be given. Applications of the theory to mathematical physics (Young-Mills equations, mirror symmetry, etc.), computer science and other fields will also be considered.
