It is wonderful to see this extraordinary work back in print, especially in this attractive low cost Dover edition. As an added bonus, the myriad misprints that plagued the original 1965 printing (and caused me such grief when I first read it in high school) have been corrected.
The path integral approach, so clearly explained in this volume, derived from Feynman's graduate research at Princeton where he applied variational principles to quantum mechanics. This, in turn, was motivated by a seminal 1932 paper of Dirac.
At the time, the formalism appeared to provide only an elegant means of deriving the wave equation without achieving any new results. But elegant mathematics always seems to have a way of finding application in physics. Just look at how formerly "obscure" topics like Lie algebras and differential geometry have become part of the essential language of particle physics. And path integral methods have proved useful in fields ranging from quantum electrodynamics to acoustic propagation.
Like all of Feynman's works, this text combines sound, if unconventional, mathematics with remarkable physical insight. There is still no better introduction to the topics treated here. This book is required reading for anyone wishing to understand quantum mechanics (at least in so far as anyone can understand quantum mechanics) and who intends to pursue more advanced topics.
Heartily recommended!