This is a corrected Dover reprint of a book first published in 1966. The main goal is to demonstrate that many of the basic laws of physics can be expressed in terms of variational principles. The first chapter tackles classical and relativistic mechanics, the second treats optics via Fermat's Principle, and the third deals with field equations in both the Lagrangean and the Hamiltonian formulations, including some quantum field theory. The final two chapters deal with discrete and continuous eigenvalue problems and scattering theory.
The original publication was reviewed by Lawrence Spruch in Mathematics of Computation, April, 1967. Spruch found the first two chapters to be, "almost of necessity", a standard treatment. He found chapter three to be "good but too terse", but he particularly liked the material on scattering theory. He concluded that the book would be useful to physics graduate students and perhaps also to mathematics graduate students who know some physics.
An author's preface in the new edition indicates that a few minor errors and misprints have been corrected, but that otherwise the text is identical to the original version. The new preface also gives a (very brief) historical account of variational methods. Overall, the book strikes me as somewhat old-fashioned but perhaps still useful, particularly to students of physics.
Fernando Q. Gouvêa is Professor of Mathematics at Colby College in Waterville, ME.