Master the advanced analysis of countable Markov chains through state-of-the-art Lyapunov function methods. This seminal work provides a self-contained introduction to the constructive theory, detailing practical approaches for constructing essential Lyapunov functions. Gain crucial insights into convergence and stability, making this text indispensable for postgraduate students and researchers in probability theory, stochastic processes, and mathematical analysis across India. Elevate your understanding of complex systems with rigorous, applicable techniques.