Stochastic Optimization plays a critical role in radio resource optimization of wireless networks, optimal control theory as well as financial engineering (portfolio optimization). This course will focus on the stochastic optimization theory and the application to the design and optimization of next generation wireless systems and federated learning applications. Topics covered include (A) Physical Layer Modeling: review of information theory for wireless fading channels, MIMO spatial diversity and spatial multiplexing, (B) Theory of Stochastic Optimization: classifications and motivating examples of stochastic optimizations [Type I stochastic Optimization and Type II stochastic optimization problems], theory of Stochastic Approximation, Stochastic Gradient, (C) Applications of Type I SO: Robust optimizations and Federated Learning: (D) Applications of Type II SO: Markov Decision Process, Stochastic Stability and Delay-optimal wireless resource control.