Review of Probability theory and stochastic processes, stochastic processes and linear systems, Gaussian random process, spectral analysis of stationary processes, Power Spectral Densities, Stationarity and Ergodicity, Optimal Linear Systems, Wiener Filters, discrete and continuous time Markov chains, discrete time branching processes, birth and death processes, random walks, large deviations and Martingales, Poisson processes, renewal processes, Brownian motion, Queueing theory Diffusion processes and stochastic differential equations, the Fokker-Planck and Langevin Equations. Applications in Communication engineering and Signal processing, Wireless systems, Detection, estimation and control, Computer networks, Optical communication, Speech modeling and recognition, Modeling of neural processes, Radar and automatic control. Other applications in epidemic, competition, predation and population genetics, mathematical finance, and processes in natural and social sciences.