This module will start with an introduction to o-minimality, assuming some basic model theory. We'll cover the Monotonicity Theorem and cell decomposition (though not with complete proofs) and then dimension of definable sets. We'll then discuss the Pila-Wilkie Theorem, which bounds the number of rational points of bounded height lying on (the transcendental part of) a definable set. We'll prove the parameterization theorem, discuss the number-theoretic results needed, and combine these to prove the Pila-Wilkie Theorem. We'll then discuss some examples of o-minimal structures and some applications of the Pila-Wilkie result.