To best of my experience, there are two different aspects for learning DFT. First is the grasp of the fundamental knowledge of the Density functional theory and second is learning the technical aspects (e.g: learning various available DFT packages) to apply DFT to real world problems. Depending on your research you may have to focus one over the another, however both are equally important. I have pasted below few books/paper which may help you to learn DFT. I hope other people will also add more.
1. For fundamental concepts of DFT (only few examples)
a. Density-Functional Theory of Atoms and Molecules; Robert G. Parr, Weitao Yang, Oxford University Press, (1989).
b. A Chemist's Guide to Density Functional Theory by Max C. Holthausen and Wolfram Koch
c. ABC of DFT by Prof. Burke: http://dft.uci.edu/doc/g1.pdf
d. A Bird’s-Eye View of Density-Functional Theory by Prof. Capelle: Article A bird's-eye view of density-functional theory
d. Books of electronic structure e.g: Electronic Structure by Richard Martin and Electronic Structure Calculations for Solids and Molecules by J. Kohanoff.
2. For practical application:
a. Density Functional Theory: A Practical Introduction :David Sholl and Janice A. Steckel (Mostly for Periodic DFT calculation)
b. Materials Modelling using Density Functional Theory Properties and Predictions by Feliciano Giustino
c. Other Computational Chemistry books (covers other methods also other than DFT) e.g:
Introduction to Computational Chemistry book by Frank Jensen
Computational chemistry book by Errol Lewars
Essentials of Computational Chemistry: Theories and Models by Christopher J. Cramer
A good method to learn DFT for beginner is to read a book and carry out some examples using a software. You can use Gaussian software and read the outstanding book of Density Functional Theory as follow: https://chemistry.fudan.edu.cn/_upload/article/files/81/27/040931c841b49c61ab6c2f7e144a/924bdd80-e6a1-40b5-8546-ab535bac2e92.pdf