Literature and Links
Books

Mikosch,T., Elementary Stochastic Calculus with Finance in View, World Scientific 1998. Based on the notes from Stochastic Calculus course he was teaching at Victoria University in Wellington.

Fries, C.P., Mathematical Finance: Theory, Modeling and Implementation, 2006. Simple
and intuitive, provides numerous examples and intuitive explanations.  Steele, J.M., Stochastic Calculus and Financial Applications, Springer 2000.

Kuo, H.H., Introduction to Stochastic Integration, Springer 2006. (Thank you Jet)
 Tavella,D., Quantitative Methods in derivative pricing: An Introduction to Computational Finance, Wiley,
2002. Chapter 2 (Fundamentals of Stochastic Calculus) of the book is a summary introduction to the basic elements of stochastic calculus. The material is presented in a nonrigorous way and should be
easy to follow by anyone with a basic background in elementary calculus.  Epps,T.W., Quantitative Finance: Its Development, Mathematical Foundations, and Current Scope, Wiley, 2009. Chapters 2 and 3 lay out some foundations.
Lecture notes
 van Handel, R., Stochastic Calculus, Filtering, and Stochastic Control, Lecture notes, Princeton University, 2007.

Shreve, S., Stochastic Calculus and Finance, Lecture notes, 1997.
 The Mathematics of Finance, Lecture notes. (Thank you Shane)

Varadhan,S.R.S., Stochastic Processes, Lecture notes, AMS 2007. (Thank you Mardi)

Quastel,J., Notes for Stochastic calculus for Mathematical Finance, University of Toronto

Bass,R., Lecture notes for Stochastic calculus, with applications to finance, PDE, and potential theory , University of Connecticut.
Schedule
Date  Discussion by  Topic  Files  
19Nov10  Vitali  Introduction  slides  handout 
17Dec10  Vitali  Conditional Expectations and Binomial trees  slides  
14Jan11  Firmin  Portfolio choice  slides  
28Jan11  Paul  ConsumptionSaving Decision with Optimal Risky Asset  slides  
11Feb11  Mardi  Jumps and Betas, discussion of Todorov and Bollerslev (2010)  link to paper  