Using molecular beam epitaxy, we have successfully developed techniques to grow various semiconductor nanostructures including quantum dots, quantum wires and quantum rings. We have also studied the physical properties of such structures. The magneto-optical properties of single quantum dots and quantum rings were investigated. We have designed and fabricated the world smallest ellipsometer, which is able to be operated at liquid He temperature and high magnetic field (14 T). Using this unique instrument, we have investigated the dielectric response of various nanostructures.