This book starts out with introducing an overview of semiconductor nanocrystals (NCs). This brief introduction will build a picture of readers from their sizes to their practical realisations. An overview about physics of semiconductor NCs is also introduced so as to make the contents of this book as self-contained as possible. The inclusion of a simple view of the pseudopotential method is also given so that when the specific calculations or applications are discussed, the basic ideas are in context. The pseudopotential approach presented in this book provides an accurate description of the complex energy level structure of InAs NCs and presents itself as a suitable tool to explain many experimental features observed in both intra- and inter-band optical absorption spectra. This book is therefore suited to not only theoretical physicists but also experimentalists who are interested in electronic and optical properties of semiconductor NCs.