This collection of papers arises from a workshop held at the "Istituto per le Applicazioni del Calcolo" of the Italian CNR. The first part of the book includes the material covered by three mini-series of lectures at graduate level on some advanced mathematical topics in semiconductor physics. The second part of the book includes more specialized topics, covered by invited speakers in their individual lectures. The volume can be used both at introductory level and as an updated and advanced review of the current literature. Most of the papers are concerned with both the macroscopic and microscopic models, ranging from the kinetic to the hydrodynamic and quantum-hydrodynamic models.