A Spoken Dialogue System (SDS) interacts with human users by interpreting spoken natural language. It responds to user speech input for answering questions, providing advice, and many other applications. Correctly interpreting user speech input is a very important task in achieving good system performance. A key issue in the task is handling ambiguity since any natural language is ambiguous. In this research, we develop a novel reinforcement learning algorithm for language disambiguation in a spoken dialogue system. In the algorithm, a machine learning agent learns knowledge about user behaviour in dialogue activities and in language use, and the knowledge is used to handle ambiguity. In this thesis, we describe the problem of ambiguity in SDSs, introduce the reinforcement learning algorithm that we developed for disambiguation, describe a spoken dialogue system for mathematics tutoring that we build to implement the algorithm, and present and analyze the experimental results.