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Aeroelasticity deals with the dynamics of an elastic structure in airflow with primary focus on the endemic instability of the structure called Flutter that occurs at high enough speed. This book presents the Continuum Theory in contrast to extant literature which is computational. §Continuum theory provides answers to What If questions which numerical codes cannot. It makes possible precise definitions such as what is Flutter Speed . Physical phenomena such as Transonic Dip for example can be captured by simple closed form formulae. And above all it can help develop intuition based on a better understanding of the phenomena of interest. Like any mathematical theory it enables a degree of generality and qualitative conclusions, increasing insight.