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This monograph provides a timely overview of recent developments in classical Lie theory as well as concrete examples in applied mathematics and mathematical physics. Utilizing a comprehensive and self-contained approach, the author provides clear explanations of the theoretical arguments on which the applications are built. Specific examples with physical applications include the cylindrical Korteweg-de Vries equations, the Navier-Stokes-Fourier equations, the three-body problem, and more. With the author's focus on the utility and algorithmic nature of Lie group analysis of differential equations, readers will gain a deeper understanding of the mathematics underpinning these applications. The author also describes and directs readers to two open source algebra packages designed to help manage these complex computations.

Lie Symmetries of Differential Equations will appeal to researchers in applied mathematics, particularly those in mathematical physics interested in exploring Lie group analysis.