About the Book: This book offers a concise introduction to stochastic processes, focusing on Markov chains and stochastic analysis. The Markov chain section emphasizes ergodicity, recurrence, and spectral gap estimates using modern techniques like coupling and duality. The stochastic analysis section covers martingales, Brownian motion, stochastic integrals, SDEs, Feynman–Kac, random time, and Girsanov transforms, linking probability to applications in MCMC, convex geometry, and number theory.