This book aims to bridge the gap between Linear Parameter-Varying (LPV) modeling and control by investigating fundamental questions of modeling and identification. It explores missing details of LPV system theory that have hindered the formulation of a well established identification framework. By proposing a unified LPV system theory, based on a behavioral approach, the concepts of representations, equivalence transformations and means to compare model structures are re-established, giving a solid basis for an identification theory. It is also explored when and how first-principle nonlinear models can be efficiently converted to LPV descriptions detailing possible pitfalls. Building on well-founded system theoretical concepts, the classical LTI prediction-error framework is extended to the LPV case via the use of series-expansion representations. The book is written as a research monograph with a broad scope, trying to cover the key issues from system theory to modeling and identification. It is meant to be interesting for both researchers and engineers but also for graduate students in systems and control who would like to learn about the LPV framework.