This lecture introduces the concept of piecewise linear payoffs for European derivatives, showing how they can be decomposed into a portfolio. It covers the proof involving a triangular system of equations, different types of payoffs such as cash, long call, and long forward contracts, and the binomial model for pricing derivatives. The lecture also explains trading strategies, including the composition of a portfolio with riskless and risky assets, the initial and terminal values of a portfolio, and arbitrage opportunities.