Book excerpt: With cutting-edge materials and minute electronic devices being produced by the latest nanoscale fabrication technology, it is essential for scientists and engineers to rely on first-principles (ab initio) calculation methods to fully understand the electronic configurations and transport properties of nanostructures. It is now imperative to introduce practical and tractable calculation methods that accurately describe the physics in nanostructures suspended between electrodes.This timely volume addresses novel methods for calculating electronic transport properties using real-space formalisms free from geometrical restrictions. The book comprises two parts: The first details the basic formalism of the real-space finite-difference method and its applications. This provides the theoretical foundation for the second part of the book, which presents the methods for calculating the properties of electronic transport through nanostructures sandwiched by semi-infinite electrodes.