In the exercises and solutions corresponding with Chapter 1 (here and in [29]), the following notions, tools, and topics are investigated or used: continuous and noncontinuous functions, upper and lower semi-continuous functions and hulls, level sets and sublevel sets, numerous special types of convex functions, epigraph, closure and interior, probability measure and space, discrete Jensen’s inequality, effective domains, subdifferential, cyclically monotonic sets (Rockafellar’s theorem), infimal convolution of functions, Minkowski sum and difference, proper functions, Asplund product, log-concave functions, Prékopa-Leindler inequality, Brunn-Minkowski inequality, support and polar functions, integrable functions, global minimum, difference body and central symmetral, and the Rogers-Shephard inequality.