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This book presents Markov chains as a practical tool in evaluating the structure of a multi-echelon educational system. It is a research-level book since its contents are too advanced for courses. The book is written at a graduate level for researchers in the field of manpower and educational planning. The impressive contributions are in the evaluation of career patterns, the attainability of structures, the estimation of transition probabilities and the development of continuous-time Markov chains from sparse matrices. For instance, in predicting enrolment, the school's differential variables are systematically inscribed in the estimation of transition probabilities. Moreover, the book identifies future research directions which may stimulate postgraduate research projects. The motivations for this book emanate from the unstable transition durations in the university system in Nigeria and the ill-posed problem of the discrete-time Markov chain in an attempt to recover the one-step transition matrix from the higher-order transition matrix. These twofold motivations are gaps in existing literature. This book attempts to bridge these gaps.