Textbook in PDF format This book provides a comprehensive overview of the current density-functional theory (DFT) for electrons in atoms and molecules, as well as a detailed review of the new formalism of the DFT. In the conventional DFT, the spatial electron distribution plays an essential role in describing the electronic properties of the system under consideration. In contrast, the electron distribution on the energy coordinate defined by the external potential applied to the electrons serves as a fundamental variable in the foundation of the new DFT. In this book, a particular emphasis is placed on the discussion on the advantage of the new theory in solving the toughest problems in the current DFT. Specifically, it is demonstrated that the new theory has a potential to solve the static correlation errors which arise in describing chemical bonds using the current DFT based on the single electronic configurations. Some prototypes of the functionals are developed in the book, which realize the static correlations. The theory is also utilized to develop the kinetic energy functional known as the most difficult issue in DFT. The book offers useful explanations of the new theory for the researchers and students to understand and apply it to future developments