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This textbook provides a simple introduction to mechanics for students coming to the subject for the first time. The text is based on courses given to first and second year undergraduates and has been written with this audience very much in mind. Prerequisites are only a basic familiarity with vectors, matrices, and elementary calculus. The author's aim is to provide an understanding of Newtonian mechanics using the tools of modern algebra. The first chapters of the book introduce the fundamentals of the motion of rigid bodies: Newton's laws, forces, linear and angular momentum, and the conservation of energy. In the later chapters the theory of Lagrangian mechanics is developed and extended to cover applications to impulsive forces. Throughout the theory is illustrated with many worked examples and numerous exercises (some with solutions) are provided.