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I have taken the occasion of a second edition for enhancements and re?- ments that preserve the spirit of the original. I have more fully portrayed the remarkable relationships between symmetry group generators and their Lie bracket and the dynamical invariants of those symmetries and their Poisson bracket in Chapter 3. The radical departure of quantum waves from classical waves is more sharply drawn in Chapter 5. The spectacular way in which the states of the hydrogen atom unfold from its symmetries is the centerpiece of qu- tum Kepler motion. I now lead readers more deliberately through this unfolding by showing how the master quantum number orchestrating fo- dimensional rotational symmetry orchestrates the hydrogen atom states. I o?er readers in Chapter 7 a more descriptive portrait of the break-up of regular Kepler motion on tori into periodic resonant points when the motion becomes chaotic. And I now include a sketch of KAM Theory— thegreatestachievementincelestialmechanicsofthetwentiethcentury—in properly?llingoutthestoryofchaoticKeplermotion. Lastly,anewedition has given me the opportunity to correct errors. The Fields of Michael and Gabriel David Oliver Meadows of Dan, Virginia, USA Autumn 2002 ix Preface to the First Edition The universe embraces with sensual presence. No thought, no word is needed to behold sky, sun, moon, stars. It is not in re?ection but in expe- encethatoneinhalestheearthysmellsofdampwoods,becomesdizzyunder the sweep of the starry night sky, basks in the sun’s warmth, rolls in ocean breakers, tastes salt. The sensual universe is open, available, immediate.

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From the reviews of the second edition: In the present book, the shaggy steed of physics is the two-body problem, a problem that guides the reader through an interesting tour of the mathematical beauty hidden in the physical world. Actually, the author takes an approach which is opposite to that usually taken by the physicist who often marvels at the physical beauty hidden in the mathematical world. This reverse approach makes the reading of this book both interesting and illuminating for the professional physicist or chemist. (Fernande Grandjean and Gary J. Long, Physicalia Vol. 57 (3), 2005) The book celebrates an unassuming bit of physics that also turns out to be an inspiring teacher. The two-body problem - the motion of two bodies bound by the inverse-square force of gravity and electricity - is the Shaggy Steed of Physics, guiding the reader to an understanding of both the forces and the mathematical beauty hidden in the physical world. ... The second edition preserves the spirit of the original while deepening key topics. (Zentralblatt fur Didaktik der Mathematik, January, 2005) This is the second edition of a very interesting little book first published in 1994. The author writes with considerable conviction, passion, and clarity on the topic of mechanics as the one major unifying theme ... . Overall, I regard this to be an excellent book, especially important for those in the community who would like to understand the big picture, the connections and the similarities between the major physical theories which describe our universe ... . (J M Hill, The Physicist, Vol. 41 (5), September/October, 2004) Oliver's new edition ... of his intellectual history of mechanics and the transition from classical mechanics to quantum mechanics enhances the first edition in several areas. ... Oliver writes elegantly, almost to the point of being flowery. ... One delightful feature not often found in works of this type is the inclusion of an appendix that contains brief technical biographies and portraits of the major contributors to the topic ... . Summing up: Highly recommended. Upper-division undergraduate and graduate students; professionals. (A. Spero, CHOICE, June, 2004)

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