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Weierstrass and Blancmange where differentiable functions, Lebesgue integrable functions with everywhere divergent Fourier series, and various nintegrable Lebesgue measurable functions. While dubbed strange or pathological, these functions are ubiquitous throughout mathematics and play an important role in analysis, t only as counterexamples of seemingly true and natural statements, but also to stimulate and inspire the further development of real analysis. Strange Functions in Real Analysis explores a number of important examples and constructions of pathological functions. After introducing the basic concepts, the author begins with Cantor and Pea-type functions, then moves to functions whose constructions require essentially neffective methods. These include functions without the Baire property, functions associated with a Hamel basis of the real line, and Sierpinski-Zygmund functions that are discontinuous on each subset of the real line having the cardinality continuum. Finally, he considers examples of functions whose existence cant be established without the help of additional set-theoretical axioms and demonstrates that their existence follows from certain set-theoretical hypotheses, such as the Continuum Hypothesis.