Finite-state methods are the most efficient mechanisms for analysing textual and symbolic data, providing elegant solutions for an immense number of practical problems in computational linguistics and computer science. This book for graduate students and researchers gives a complete coverage of the field, starting from a conceptual introduction and building to advanced topics and applications. The central finite-state technologies are introduced with mathematical rigour, ranging from simple finite-state automata to transducers and bimachines as ‘input-output’ devices. Special attention is given to the rich possibilities of simplifying, transforming and combining finite-state devices. All algorithms presented are accompanied by full correctness proofs and executable source code in a new programming language, C(M), which focuses on transparency of steps and simplicity of code. Thus, by enabling readers to obtain a deep formal understanding of the subject and to put finite-state methods to real use, this book closes the gap between theory and practice.