In physics we do things and afterwards worry about whether they worked
Feynman’s path integral formulation is important in quantum physics. Some people learn it when they come to do Quantum field theory where it plays a central role. However, there is a book that introduces a sophisticated physics student with reasonable background to path integral in non-relativistic quantum mechanics, “Quantum mechanics and path integrals”, by Feynman and Hibbs.
It is highly recommended. It is a book full of deep and extraordinary insights, as one expects from Feynman. It is not a standalone textbook in QM – it should be used in conjunction with a conventional text.
What I love the most about this book is how quickly the laws of physics are laid out – by the end of chapter 2 they are in place, and the rest of the book is applications. It is an approach similar to the one he adopts in Vol. 2 of Feynman Lectures on Physics where Maxwell’s equations are laid before you in their finished form in the first chapter and the rest of the book is devoted to understanding those equations.
The original edition, 1967, was riddled with errors. The new one is amended and available on Amazon at the end of September this year, and being a Dover costs an agreeable £15. Should you happen to come across the first edition, Daniel Styer’s errata is an absolute must. It is available here.