Intended for undergraduate mathematics students and teachers, How it All Began provides an introduction to the history of various branches of mathematics, the lives of the mathematicians, and the challenges they faced. This new work explores the great Greek legacy, Indian arithmetic, Integral Calculus, the Analytic Geometry of Rene Descartes, Differential Calculus, the Non-Commutative Algebra of Hamilton, the arithmetization of analysis, and the beginnings of Algebra.