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Non-central forces have a wide variety of applications in classical and quantum mechanics as demonstrated in this book. The author emphasizes the study of time-dependent potentials, predominantly in two dimensions, without neglecting the quite well understood time-independent case. The construction of invariants in the classical case and the study of solutions to Schroedinger's equation, as well as a detailed presentation of various mathematical techniques are of main concern to the author. The book addresses theoretical physicists and mathematicians, but it will also be useful for electrical and mechanical engineers.