We will use (parts of) the book:
I.Karatzas and S.Shreve: Methods of Mathematical Finance, 1998, 2nd Edition. Springer. ISBN: 0-387-94839-2. that can be considered as a textbook for the course.
The following book can also be consulted at the library for some aspects of related concepts:
I.Karatzas: Lectures on the Mathematics of Finance, 1997. Amer.Math.Soc..
As for some background material in stochastic calculus the following two books can be referred to:
B. Øksendal: Stochastic Differential Equations, 2007, 6th Edition. Springer. ISBN: 978-3-540-04758-2.
I.Karatzas and S.Shreve: Brownian Motion and Stochastic Calculus, 1998, 2nd Edition. Springer. ISBN: 0-387-97655-8.
Though any book in stochastic calculus can be equally be valid.