Focuses on the construction of optimal investment strategies in a security market model where the prices follow diffusion processes. Beginning with presenting the complete Black-Scholes type model, the book moves on to incomplete models and models including constraints and transaction costs. The methods and models presented include the stochastic control method of Merton, the martingale method of Cox-Huang and Karatzas et al, the log optimal method of Cover and Jamshidian, the value-preserving model of Hellwig, and so forth. Stress is laid on rigorous mathematical presentation and clear economics interpretation while technicalities are kept to a minimum.