The goal of this book is to informally introduce elementary Stochastic Calculus to senior undergraduate students in Mathematics, Economics and Business majors. The main idea was to capture as much as possible of the spirit of elementary Calculus, at which the students have been already exposed in the beginning of their majors. This assumes a presentation that mimics similar properties of deterministic Calculus as much as possible, which facilitates the understanding of more complicated concepts of Stochastic Calculus. Topics covered: Basic notions, Useful stochastic processes and their main properties, Stochastic Integration and methods of integration, stochastic differential equations, Applications of Brownian motion, Application to physics, chemistry, and filtering theory. An important feature of this textbook is the large number of solved problem and examples designed to help the reader further understand the material. Book jacket.