Introduction -- Monte Carlo Method for Solving PDE -- A Monte Carlo Algorithm for the Telegrapher's Equations -- Basics of Floating Random Walk Method for Capacitance Extraction -- Pre-Characterization Techniques for FRW Based Capacitance Extraction -- Fast FRW Solver for 3-D Structures with Cylindrical Inter-Tier-Vias -- Fast FRW Solver for Structures with Non-Manhattan Conductors -- Technique for Capacitance Simulation with General Floating Metals -- Markov-Chain Random Walk and Macromodel-Aware Capacitance Extraction -- GPU-Friendly FRW Algorithm for Capacitance Extraction -- Distributed Parallel FRW Algorithm for Capacitance Simulation -- A Hybrid Random Walk Algorithm for 3-D Thermal Analysis.