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Understanding the leaf venation network is a multifaceted endeavor that requires tools from several fields of study. This thesis addresses a broad range of questions, all guided by a central theme: “How does the geometry and topology of leaf venation depend on its function, development, and evolution?”. The aim of this thesis is to make a small contribution towards answering this immensely broad question and naturally, not every question can be answered. We attempt a multi-pronged approach that we hope can serve as a first stepping stone to more integrative studies in the future. To begin to attack it, it is necessary to break the question down into smaller pieces that can be addressed individually. We ask, broadly, “What is the connection between the geometry and the topology of leaf networks?”, and “What is the connection between the physics of evolution and development of leaf networks?”. This work provides a modest contribution to the science of plant vasculature from a physicist’s perspective. We topologically analyze a data set of leaf venation networks, model topology and development, and provide an evolutionary perspective one network form and function. Advisors/Committee Members: Katifori, Eleni (advisor), Katifori, Eleni (referee), Zippelius, Annette (referee).