Semiconductor nano－structures are an important type of nano－material that will become the core of the next generation of micro－electronic and opto－electronic devices. There are various kinds of such nano－structures, for example, self－assembled quantum dots, nano crystallites and silicon clusters, which can be used to fabricate nano－electronic devices. Based on these nano－structures, our NNSFC funded project proposed four theories for studying their electronic structures, and found many new effects regarding their electronic states and physical properties. These theories include: one－dimensional quantum waveguide theory, effective－mass theory of isolated quantum dots and quantum wires, hole effective－mass theory for hetero structures, and empirical pseudopotential homo－junction models. The monograph Semiconductor Superlattice Physics presents a comprehensive introduction to the concepts, principles, theories, and experimental results of semiconductor superlattice physics, with a special summary of our group′s theoretical research results in this area.