This is a textbook on Montague-style compositional semantics in a generative syntactic framework that covers such areas as compositionality, intersective vs. non-intersective predicates, anaphora, and quantifiers. The emphasis is on using the theory of types to implement these ideas, so this is a good book from which to learn lambda calculus. There isn't much on world-relative assignment functions (see the textbook Introduction to Natural Language Semantics for this), and intensional semantics only gets a brief treatment in a concluding chapter. (Apparently Heim and Kratzer have a separate textbook on intensional semantics in manuscript.) As in many advanced linguistics textbooks, Heim and Kratzer adopt a Socratic method, exploring various theoretical alternatives in each chapter before settling on their preferred solution. The exposition is clear and there are exercises throughout. This book would be a suitable sole text for an advanced undergraduate or graduate semantics course.



Errata:
The exercise at the end of chapter 9 on page 257 has an incorrect definition of only. In a situation in which there were two people, John and Bill, neither of whom could start the car, the sentence Only Bill could start the car would be true. A better definition would be:

[[only]] = λx. λf. for all y such that y ≠ x, f(y) =0, and f(x) = 1