This book presents the classical theory of asset pricing for European and Asian options. The mathematical content is simplified as much as possible for an easy access by non-mathematicians students and practitioners. Each concept is introduced with an emphasize on intuition and financial meaning, as a result of my extensive teaching experience with master’s students from economics, finance and computer science for finance. The Black and Scholes model is naturally described and, more generally, the local volatility models, which are constructed from standard Brownian motions. Numerical implementations to price contingent claims under a risk-neutral probability measure are provided in the Python programming language. At last, we present a recent alternative to price a European claim in a discrete time model that does not need any risk-neutral probability measure.