This course presents the fundamentals of probability theory and stochastic processes. Contents of this course are relevant to several disciplines including statistics, communications and information systems, computer engineering, signal processing, machine learning, bioinformatics, econometrics, and mathematical finance. Contents: I- Review of Probability theory Introduction and basic probability; Discrete Random Variables; Continuous Random Variables; Multivariate Distributions; Moment- generating functions and characterstic functions; Inequalities and bounds for random variables. II- Introduction to Random Processes Introduction and basic concepts; stationarity and ergodicity; covariance functions; Poisson processes; Gaussian processes; Spectral representations; Linear filters; Integration and differentiation of stochastic processes; ARMA models; Markov chains; Queuing theory.