The lectures are focused on analytical and numerical methods for pricing financial derivatives like options on underlying stocks. Starting from the classical Black-Scholes equation for pricing vanilla options we focus on path dependent options including pricing of American style options, Asian and barrier style of options. The methodology how to price such financial instruments is based on solving partial differential equations. In some cases the underlying equation can be solved analytically. In the case of American style and path dependent options the solution is provided by means of numerical approximation scheme.