The monograph is devoted to a new theory of differential calculus, organically and naturally including three components: finite, infinite and continual theory of differential calculus. The new triune theory overlaps multiply the classical theory scope of application due to that unlike the classical theory which is focused exclusively on the function, the author theory is focused both on function and function increments, and increments of any order. The offered theory has perfect theoretical and practical proofs and study. The book is available for a wide range of readers - from the leading experts in mathematical analysis to schoolchildren of secondary schools.