General relativity with focus on action?

I am having a class of general relativity. It seems that the professor will follow an approach which consist of achieve the action, and variate it to get the equations of motion (indeed, that's how we already got the geodesic equation, the dynamics of a particle in electromagnetism, the equation of the fields itself, and the action of massless particle, etc...). Do you know any book that follows such approach? That is, a book that focus mainly on the action of the fields itself.

Dirac derives GR equations from the principle of action.

Nearly every book on GR discusses the action: Carroll, Wald, d'Inverno, etc. Which book do you use?

My favorite for introductory GR is Landau+Lifshitz vol. 2. He uses the action principle to derive the Einstein field equation. The Hilbert action is the most simple heuristic argument for why these equations should look as they look.

Introduction to General Relativity by Bambi.

Excerpt from a book description:

"Following the approach of Lev Landau and Evgenii Lifshitz, this book introduces the theory of special and general relativity with the Lagrangian formalism and the principle of least action."

I found the book quite readable and going
straight to its object.

vanhees71 said:

My favorite for introductory GR is Landau+Lifshitz vol. 2. He uses the action principle to derive the Einstein field equation. The Hilbert action is the most simple heuristic argument for why these equations should look as they look.

I agree that LL vol 2 is good. You mention Hilbert action as a heuristic argument. Is heuristic the right word here. I thought of Einsteins intuitive manner of developing his equations as heuristic. I would regard Hilbert's development as quite formal.

What you call "heuristic" is pretty much a question of your preknowledge. For me the action principle is the most versatile tool to guess equations of motion given a symmetry principle and I think it's much more "intuitive" or "heuristic" than Einstein's derivation.