Computability, An introduction to recursive function theory

This book is an amazing and seemingly comprehensive introduction. I used this book to fill in gaps in my knowledge before writing a paper on analytic computability. As a fan of the Lambda calculus and associated styles of computing this book using the Turing machine (automata) approach. I am not apposed to this I simply like the more Logic style. That is my only complaint, the book is well written and incredibly engaging with bite size exercises and full intuition sections. This was a breath of fresh air from the Conway, Hodel style books that are more rigorous and comprehensive but dense. This book also acts as a refresher as I begin to examine Weihrauch’s computable analysis.

This book does an amazing job early on of tying the notion of computability to $\mathbb{N}$, examining Diophantine equations in the context of decidability.