Properties of low-dimensional electron systems at low-temperatures and/or at high magnetic fields are studied. We fabricate various one- and zero-dimensional systems in semiconductor nanostructures, and study the electronic properties: phase diagram of electronic states and spin-spin correlation effects such as Hund’s rule and the Kondo effect in artificial atoms, molecules and Tomonaga-Luttinger liquid effects in quantum wires and so on. Control of spin effects and its application to quantum computation are also interesting topic under investigation. We are developing a scanning probe technique available at low-temperature and high- magnetic field to monitor the spatial distribution of electronic density of states.