Abstract: Finite-state methods are well established in language and speech processing. OpenFst (available from www.openfst.org) is a free and open-source software library for building and using finite automata, in particular, weighted finite-state transducers (FSTs). This tutorial is an introduction to weighted finitestate transducers and their uses in speech and language processing. While there are other weighted finite-state transducer libraries, OpenFst (a) offers, we believe, the most comprehensive, general and efficient set of operations; (b) makes available full source code; (c) exposes high- and low-level C++ APIs that make it easy to embed and extend; and (d) is a platform for active research and use among many colleagues.