What is the New Keynesian Approach?

I received a comment on the previous post (link) asking about the new Keynesian approach. So, let me try to provide some information based on the author's explanation of this concept. According to Walsh, the new Keynesian approach employs equilibrium models with some frictions or rigidities. He says, the new Keynesian approach uses

models based on dynamic optimization and nominal rigidities in consistent general equilibrium framework.

The monetary frictions or rigidities that Walsh refers include

money-in-utility function, cash-in-advance, search model of money, informational, portfolio, and nominal rigidities, and credit frictions,

which are all discussed in the book.
Another essential book on the new Keynesian monetary economics, written by one of the leading researchers in the field, is the following. This might also be useful for students and central bank economists alike.