Singularity theory is a meeting point of various areas of mathematics and science in general. New discoveries and striking developments are happening day-to-day, both within singularity theory itself and in its relations with other areas of mathematics. The purpose of this event is to present some of the basic foundations of singularity theory, as well as up-to-date material that brings us up to the boundary of our present knowledge in various topics. Particular emphasis will be given to the geometric and topological aspects of the theory. The School and Workshop will concern singularities in both complex and real geometry. As such, it provides a natural continuation of previous schools in singularities held at ICTP in 1991 and more recently, in Summer of 2005. The themes and specific topics will include: lagrangian and legendrian singularities, relations with knot theory, stratifications of analytic spaces, topology of singular spaces, gauge theory and new manifold-invariants, contact and symplectic geometry, resolutions of singularities, toric varieties and topological invariants of algebraic varieties. The first week (8-13 January) will consist of elementary lecture courses. The second week (15-20 January) will be organized into advanced lecture courses and there will be also research seminars and conferences during this week. A workshop will be held during the third week (22-27 January), with the participation of renown experts and a course delivered by Professor Heisuke Hironaka. Moreover, the conference will be a celebration of the first 60 years of Professor Lê Dũng Tráng