In this seminar we survey discrete time, multi period, sequential investment strategies for financial markets. Under memoryless assumption on the underlying process generating the asset prices the Best Constantly Rebalanced Portfolio is studied, called log-optimal portfolio, which achieves the maximal asymptotic average growth rate. For generalized dynamic portfolio selection, when asset prices are generated by a stationary and ergodic process, universally consistent empirical methods are shown, using current principles of nonparametric regression estimation and machine learning algorithms. The empirical performance of the methods are illustrated for NYSE data.