Brownian motion and stochastic calculus

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The all time classic at the level your looking for is William Feller's two volume set "Introduction to probability theory and its applications"- if you can find a copy. A good university library should have a copy. On wikipedia, it claims that Persi Diaconis (of the seven shuffles theorem fame) was motivated to finish high school after dropping out so that he could understand the contents of this book. 'nuff said. Karatzas and Shreve "Brownian Motion and Stochastic Calculus" is also a popular book among quants.