The theory of computing can be a difficult subject to master, because of the densely symbolic notation and the mathematical complexity of the concepts. When I was a graduate student preparing for the theory portion of my exams, I remember being dismayed at the choice of textbooks that was available at the time: most simply threw a collection of Greek letters and subscripts at the reader, with little attempt to provide simply-worded explanations that would give the reader an intuition for the concepts.
Now that I am teaching the theory of computing, I want to provide my students with the best textbook I can find.
Two years ago, I was delighted to find R. Gregory Taylor's new book, "Models of Computation and Formal Languages". This is by far one of the most readable theory textbooks I have encountered. One of the features that caught my eye when I first examined the book was that many of the complicated symbolic expressions are accompanied by little explanatory text boxes with arrows that point to a symbol in the expression and explain the symbol that the arrow points to. I do this in class when I am lecturing -- I point to various symbols and explain where they came from, sometimes jotting down notes on the board alongside the symbols -- but this is the first time I have seen this technique in a textbook.
The writing style of the book is also fairly friendly and informal, without compromising mathematical precision.
The coverage of Turing-equivalent computing models is broader than in most introductory theory books; Taylor includes chapters not only on Turing Machines, but also on Recursive Function Theory, Markov Algorithms, Register Machines, Post Systems, and a model of parallel computation. Additionally, most chapters end with a proof that the model presented in that chapter is computationally equivalent to Turing Machines; thus, by the time the Church-Turing thesis is introduced in chapter 8, the reader is well prepared to entertain the claim that all of these models are capturing the same basic notion of an "algorithm".
I highly recommend this book to readers who want a readable introduction to computability theory.