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The Lagrange formalism forms the basis of modern theoretical physics. Its usefulness in solving mechanical problems in particular lies in the fact that it is based on a scalar quantity, the so-called action, and therefore offers a vector-free formulation. The realm of applications is myriad. In this book we concentrate on its usage in classical mechanics, starting with basic principles, discussing particle dynamics, then rigid bodies. Thereafter, we devote a full chapter to small oscillations. We touch on fluid motion and the theory of relativity, before, in the final chapter, elucidating the connection to Hamilton's theory. Each chapter is more or less self-contained. We have presented many example problems, but also include a list of (unsolved) problems at the end of each chapter.