chapter Introduction: basic concepts -- chapter 1 Cantor and Peano type functions -- chapter 2 Functions of first Baire class -- chapter 3 Semicontinuous functions that are not countably continuous -- chapter 4 Singular monotone functions -- chapter 5 Everywhere differentiable nowhere monotone functions -- chapter 6 Nowhere approximately differentiable functions -- chapter 7 Blumberg’s theorem and Sierpin´ski-Zygmund functions -- chapter 8 Lebesgue nonmeasurable functions and functions without the Baire property -- chapter 9 Hamel basis and Cauchy functional equation -- chapter 10 Luzin sets, Sierpin´ski sets, and their applications -- chapter 11 Absolutely nonmeasurable additive functions -- chapter 12 Egorov type theorems -- chapter 13 Sierpin´ski’s partition of the Euclidean plane -- chapter 14 Bad functions defined on second category sets -- chapter 15 Sup-measurable and weakly sup-measurable functions -- chapter 16 Generalized step-functions and superposition operators -- chapter 17 Ordinary differential equations with bad right-hand sides -- chapter 18 Nondifferentiable functions from the point of view of category and measure.