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This tutorial will provide a brief introduction to key concepts and mathematical models in community ecology, with an eye towards understanding microbiomes. We will introduce Consumer Resource Models (CRMs) and generalized Lotka-Volterra equations, emphasizing overarching ecological concepts, graphical methods, and connections to optimization. The last part of the tutorial will focus on shortcomings of these classical models for understanding microbial systems, and in particular discuss how metabolism naturally couples species and their environments through ubiquitous cross-feeding necessitating modifications of classical ecological models.