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In this talk we discuss concentration inequalities that estimate deviations of functions of independent random variables from their expectation. Such inequalities often serve as an elegant and powerful tool and have countless applications. Various methods have been developed for proving such inequalities, such as martingale methods, Talagrand's induction method, or Marton's transportation-of-measure technique. In this talk we focus on the so-called entropy method, pioneered by Michel Ledoux, that is based on some simple information-theoretic inequalities. We present the main steps of the proof technique and discuss various inequalities and some applications.