Universal prediction of sequences – the stochastic setting and the individual setting. Relation between source coding and prediction. Universal source coding – Kriechevski-Trofimov’s approach, Lempel-Ziv, Context Tree Weighting (CTW) and Prediction by Partial Matching (PPM) algorithms. Prediction/sequential decision with general loss functions. Relation to game theory. “How to use expert advice”? The Minimum Description Length (MDL) principle, Occam’s Razor and Kolmogorov’s complexity. Financial prediction and the portfolio problem. Prediction and Coding with large/unknown alphabet. Universal filtering and universal “de-noising”. Relation to empirical Bayes and related statistical methods. Universal hypothesis testing. Communication over unknown channel and individual channels – universal decoding, universal communication with feedback. Open current problems.