I believe too much is made of the Hohenberg-Kohn theorem -expressing the ground-state energy as a function of the density alone in the manner E[ρ] is unhelpful and obfuscates the theory. We do not ever attempt to obtain the energy is this manner, by some miraculous use of the Hohenberg-Kohn theorem. The constrained-search approach is a much more intuitive and transparent introduction to DFT and the theory of Lieb provides an elegant mathematical framework that captures the essence of DFT. The Hohenberg-Kohn theorem 5 is ubiquitous, but little used in practice. Its proper place today is in review articles and textbooks, and we should focus on the constrained-search approach and the formulation of DFT in terms of Legendre transforms. Kutzelnigg's "beginner's" guide to the latter is accessible to most in the DFT field. As noted in contribution (2.1.13), "the power of DFT derives from Kohn-Sham theory," but the successes of Kohn-Sham theory are linked closely to the ability of local density approximations to the exchange-correlation energy E xc to give useful results in most cases. Kohn noted: "I believe that formal DFT would have been of very little interest if there had not been a simple and very practical approximation for E xc , the LDA, which has yielded surprisingly accurate results." Kohn and Sham proposed using an LDA for E xc that is exact in two limits (slowly varying densities and high densities). These are far from the density distributions found in atoms, molecules, and condensed matter. Kohn and Sham, and many others, were therefore convinced that LDAs would not describe chemical bonding well. Nevertheless, they gave "reasonable" answers in early tests of energy differences (including small molecules and jellium half-spaces ) and remain the basis of many approximations for E xc . The initial successes of LDA were so surprising that they motivated work to understand why it could provide useful energy differences for systems with densities far from the regions of obvious validity. This work led to "adiabatic coupling" and studies of the exchange and correlation holes, their spherical averages and related sum rules, which have been of lasting value in DFT studies. This surprisingly satisfactory description of reality often provided by LDAs was essential to the ultimate success of DFT.