  The goal of this book is to present classical mechanics, quantum mechanics,
and statistical mechanics in an almost completely algebraic setting, thereby
introducing mathematicians, physicists, and engineers to the ideas relating
classical and quantum mechanics with Lie algebras and Lie groups. The book
emphasizes the closeness of classical and quantum mechanics, and the material
is selected in a way to make this closeness as apparent as possible.
  Much of the material covered here is not part of standard textbook treatments
of classical or quantum mechanics (or is only superficially treated there). For
physics students who want to get a broader view of the subject, this book may
therefore serve as a useful complement to standard treatments of quantum
mechanics.
  Almost without exception, this book is about precise concepts and exact
results in classical mechanics, quantum mechanics, and statistical mechanics.
The structural properties of mechanics are discussed independent of
computational techniques for obtaining quantitatively correct numbers from the
assumptions made. The standard approximation machinery for calculating from
first principles explicit thermodynamic properties of materials, or explicit
cross sections for high energy experiments can be found in many textbooks and
is not repeated here.
