Macroeconomics Textbook on New-Keynesian models I'm looking for textbooks that explain the New-Keynesian models, without taking shortcuts on the mathematics, that would go in depth on the derivations of the formulas. I appreciate rigour, and clarity above all else. If intuition is supplied, it would be perfect.

I find Jordi Galí's book on monetary policy is not good at presenting the model, specially by not explaining the mathematical assumptions (which are not simple details...)

Edi:
Check the link found here
Michael Woodford's book Interest and Prices, while it may not be explicitly New Keynesian, may have some of the rigor you're looking for applied to this class of models.

A more direct alternative would be New Keynesian Economics edited by Mankiw and Romer. While it's a collection of papers not a textbook, if you're looking for underpinnings of New Keynesian models this'd be a good place to start. Also "The Science of Monetary Policy: A New Keynesian Perspective" by Clarida, Gali and Gertler.