Peter Smith has a pretty good handout on Tennenbaum's theorem that I found useful when learning that material. As others have mentioned, Richard Kaye's Models of Peano Arithmetic is the go-to reference work here. Kossak and Schmerl's The Structure of Models of Peano Arithmetic is meant to give the state of the art circa 2006, but you probably won't need this one.

Peter Smith has a pretty good handout on Tennenbaum's theorem that I found useful when learning that material. As others have mentioned, Richard Kaye's Models of Peano Arithmetic is the go-to reference work here. Kossak and Schmerl's The Structure of Models of Peano Arithmetic gives the state of the art, but you probably won't need this one.