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Talk Abstract: Markov chains represent a versatile tool for modelling phenomena in nature and technology. Many phenomena unfold on several time scales. In this talk I first give an accessible introduction to Markov chains and in particular to singularly perturbed Markov chains, which are stochastic dynamical models with several time scales. Then, I demonstrate the application of singularly perturbed Markov chains to queueing systems, web ranking and reinforcement learning.