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This book consists of five chapters and four appendixes. Each chapter ends with many excellent references. The first chapter is an introduction and historical literature review. There have been few attempts like this to assemble the literature and present a systematic framework for the control of underactuated mechanical systems (UMSs). Although this chapter does not cover all of the vast number of techniques that are available, it does provide many references for those not described. The second chapter covers generalities and the state of the art on the control of UMSs. The third chapter presents UMSs from the Lagrangian formalism. who are experts in IEEE fields of interest or in history can request a guest account for editing access. The fourth chapter details the two main methods for classifying the UMSs and explores the possibility of a link between them. The key steps of each method are laid out, and several examples are provided, further aiding in cementing the reader??s understanding. In the fifth and final chapter, the authors describe control approaches to address all of the classifications within the CFD method.