List of definitions and results you should know.
The above can all be found in:
Bernt ?ksendal: Stochastic Differential Equations, 2003. Springer. (6th Edition).
Chapters: 2, 3, 4, 5, 7.1, 7.2, 7.3, 7.4, 8.1, 8.2, 8.6 , Appendix A and B.
Supporting literature:
S.R.S. Varadhan: Probability Theory, 2001. Courant Lecture Notes in Mathematics
Chapters: 5.1, 5.3 and 5.4.
and
I. Karatzas and S.E. Shreve: Brownian Motion and Stochastic Calculus. Springer. (2nd Edition).
Chapters: 1.2, 1.5, 3.3 B and 5.3 B.
Additional material:
The local property of the Ito integral (NB: new version as of 7th of May)
Alternative description of the Brownian Motion
Dependence on initial value of SDEs