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This manuscript is designed for an introductory course in the financial mathematics. The purpose of this work is to introduce foundation financial mathematics contents to undergraduate as well as to master students with Mathematics, Economics and finance majors. This syllabus contains a guide of a course in Financial Mathematics content. It aimed at financial mathematics students who need an introductory course on theory of interest rate, Partial Differential Equation, probability theory stochastic process, insurance/Actuarial Science, gambling theory stochastic calculus and Wald`s theory which are necessary steps towards understanding financial mathematics and are centered around Financial Mathematics and have been used to model a variety of different phenomena in Finance and Economics. This book will be attractive to both finance and Economics students, who might get lost otherwise in a very profound mathematical textbook.