This is an introductory lecture on some very basic principles of density functional theory, and some basic properties of density functional approximations. Useful references are "DFT in a nutshell", for beginners with any background, "A perspective on DFT" for a survey of the field a few years ago, and "The ABC of DFT", my long online unfinished textbook draft. All are available at http://dft.uci.edu.
Another useful resource is the video of my lectures in Israel, available at https://www.weizmann.ac.il/materials/Leeor/tutorials.
Slides and notes