Description: The book can be thought of as giving both a first and a second course in type theory. We begin with introductory material on logic and functional programming, and follow this by presenting the system of type theory itself, together with many examples. As well as this we go further, looking at the system from a mathematical perspective, thus elucidating a number of its important properties. Then we take a critical look at the profusion of suggestions in the literature about why and how type theory could be augmented. In doing this we are aiming at a moving target; it must be the case that further developments will have been made before the book reaches the press. Nonetheless, such an survey can give the reader a much more developed sense of the potential of type theory, as well as giving the background of what is to come.
