[Author] Apushkinskaya, D. E.; Nazarov, A. I. [Title] Around the Normal Derivative Lemma [AMS Subj-class] 35B50 Maximum principles in context of PDEs 35J15 Second-order elliptic equations 35B53 Liouville theorems and Phragmén-Lindelöf theorems in context of PDEs 35R11 Fractional partial differential equations [Keywords] strong maximum principle, the Hopf--Oleinik lemma, the Harnack inequality, the Aleksandrov--Bakel'man maximum principle [Abstract] This is a survey. It describes the history and present state of one of the most important fields in the qualitative theory of elliptic partial differential equations related to the Strong Maximum Principle and Boundary Point Principle (the normal derivative lemma). Bibliography: 359 titles [Comments] LaTeX, Russian, 96 pp. [Contact e-mail] al.il.nazarov@gmail.com