A thorough exploration of properties related to differentiation is undertaken in this chapter. Dini derivates of a function are defined, and their properties, including measurability of Dini derivates, are studied. Topics covered monotone functions, functions of bounded variation, absolutely continuous functions, monotonicity theorems, and their consequences. Also, characterizations of indefinite Lebesgue integrals and indefinite Riemann integrals are made. Integration by parts and change of variables for Lebesgue integration are discussed. Points of density of a set and approximately continuous functions are introduced, and it is proved that a function f is measurable if and only if f is approximately continuous almost everywhere. Properties of approximately continuous functions are studied.