TITLE: Where to begin in approaching Stochastic Calculus?
QUESTION [16 upvotes]: I have experience in Abstract algebra (up to Galois theory), Real Analysis(baby Rudin except for the measure integral) and probability theory up to Brownian motion(non-rigorous treatment). Is there a suggested direction I can take in order to begin studying stochastic calculus and stochastic differential equations?

REPLY [4 votes]: There are several textbooks out there for finance professionals that do not require heavy understanding of measure theory (don't require any).  I think there is an unconscious bias of math professionals to want to learn the theory.  But it's totally not required.  Just as an engineer can learn to solve integers and solve them well with lots of tricks, never having done theoretical calculus, so can you very easily learn the major methods of stochastic calculus, with no more prereqs than what you already have.
E.g. see https://people.emich.edu/ocalin/Teaching_files/D18N.pdf
BTW, nothing stops you from going back later and learning a bunch of rigor theory stuff.  But why not go now and get the basic manipulational skills.  They will do you more good in any sort of finance job.  And it preserves option value (decide to invest in the rigor later when you know you need it.)  
Actually I would even go further and say that you are more likely to succeed in learning the material, to learn it deeply, and even time efficiently, if you do it the "easy way" first and move only to rigor as a progression.