Option Theory with Stochastic Analysis : An Introduction to Mathematical Finance The objective of this textbook is to provide a very basic and accessible introduction to option pricing invoking only a minimum of stochastic analysis. Although short it covers the theory essential to the statistical modeling of stocks pricing of derivatives (general contingent claims) with martingale theory and computational finance including both finite difference and Monte Carlo methods. The reader is led to an understanding of the assumptions inherent in the Black & Scholes theory of the main idea behind deriving prices and hedges and of the use of numerical methods to compute prices for exotic contracts. Finally incomplete markets are also discussed with references to different practical theoretical approaches to pricing problems in such markets. The authors style is compact and to the point requiring of the reader only basic mathematical skills. In contrast to many books addressed to an audience with greater mathematical experience it can appeal to many practitioners e.g. in industry looking for an introduction to this theory without too much detail. It dispenses with introductory chapters summarising the theory of stochastic analysis and processes leading the reader instead through the stochastic calculus needed to perform the basic derivations and understand the basic tools It focuses on ideas and methods rather than full rigour while remaining mathematically correct. The text aims at describing the basic assumptions (empirical finance) behind option theory something that is very useful for those wanting actually to apply this. Further it includes a big section on pricing using both the pde approach and the martingale approach (stochastic finance). Finally the reader is presented the two main approaches for numerical computation of option prices (computational finance). In this chapter Visual Basic code is supplied for all methods in the form of an add in for Excel. The book can be used at an introductory level in Universities. Exercises (with solutions) are added after each chapter