This introduction presents an overview of the key concepts discussed in the subsequent chapters of this book. The book explores on dependency phonology, and examines its connections with other non-linear proposals. It provides a useful comparative synthesis of some of the issues raised by John Anderson, Heinz Giegerich and Nigel Vincent. The book discusses the nature of the internal structure of segments and argues that the richer internal structure assigned to segments in dependency phonology renders unnecessary the positing of tiers basic to CV phonology. It focuses on Tridirectional Feature Systems for Vowels — puts forward a system where the basic components for the description of vowels are related to the dependency primitives but in a binary notation. The book provides a theory-internal discussion of intrasegmental structure. It considers in detail whether a hierarchical representation of suprasegmental structure could be replaced by an approach based on the notion of 'grid'.