The aim of the course is to explain in very simple - namely discrete time - settings the fundamental ideas of modelling of financial markets and pricing of derivative securities using the principle of no arbitrage. Even the simplest of all models with only one time step allows several important notions to be illustrated. The module progresses with more complex models - with many time steps and several stocks - which are developed along with the corresponding theory of pricing and hedging derivative securities such as options or forwards. Relatively simple mathematical considerations lead to powerful notions and techniques underlying the theory - such as viability, completeness, self-financing and replicating strategies, arbitrage and equivalent martingale measures. These are directly applicable in practice, particularly in the continuous time limiting theory developed in a subsequent module. The general methods are applied in detail in particular to pricing and hedging European and American options within the Cox-Ross-Rubinstein (CRR) binomial tree model. The Black-Scholes model as the limit of CRR models is discussed to pave the way for the continuous time theory.