The course will start with an overview of finance, importance of efficient financing and securities as the means of this. Afterwards the fundamentals of probability theory will be covered, Brownian motion as the main tool of modeling asset prices will be introduced and developed. Combining this model and probability theory with basic principles of asset pricing we will deduce price formulas for different types of securities. We then will develop the machinery of calculus for Brownian motion paths, and apply it to asset pricing.