For a complete minicourse on DFT++ including exercises, you may go here.Briefly, DFT++ is a new formalism for performing ab initio quantum mechanical calculations for density functional-like systems. It is linear algebraic, basis independent, and fully explicit, making the transition from physical expression and mathematical derivation to computer coding very easy and straightforward.
Note that in adding the many new features into DFT++3.0 (such as dual plane wave/wavelet capability) the code has drifted somewhat from the original philosophy in order to optimize memory usage. We plan to fix this soon in an upcoming release. [See our contribution wish list.]
Historically, the use of DFT++ for the creation of this software was started as part of the thesis work of Sohrab Ismail-Beigi at MIT in Prof. Tomas Arias's research group. The starting version uses plane waves, but as the formalism is basis dependent, this is no real restriction. A wavelet version is in the works.