Density Functional Theory is a mainstream electronic structure theory of many-electron systems, which has achieved a high-level sophistication. In this theory, everything is known except for the exchange-correlation component, which has to be approximated as a functional of the electron density. Therefore, the subject of this theory has been the development of more accurate exchange-correlation functionals. This book is based on the dissertation of the author for his graduate study at Tulane University. In this book, the author describes the theoretical underpinnings of the theory. Then he discusses how to develop accurate density functionals with constraint satisfaction approach. The method is illustrated with the construction of accurate density functionals. Some of the work (chapter 7) is presented for the first time. Inspired by the work discussed in this book, he and collaborators developed a uniformly-accurate meta-generalized gradient approximation called TPSS functional (from the authors'' initials), which has been coded in all major computer programs and has been widely used in electronic structure calculations.