The goal of this book is to emphasize the formal statistical features of the practice of equating, linking, and scaling. The book encourages the view and discusses the quality of the equating results from the statistical perspective (new models, robustness, fit, testing hypotheses, statistical monitoring) as opposed to placing the focus on the policy and the implications, which although very important, represent a different side of the equating practice. The book contributes to establishing "equating" as a theoretical field, a view that has not been offered often before. The tradition in the practice of equating has been to present the knowledge and skills needed as a craft, which implies that only with years of experience under the guidance of a knowledgeable practitioner could one acquire the required skills. This book challenges this view by indicating how a good equating framework, a sound understanding of the assumptions that underlie the psychometric models, and the use of statistical tests and statistical process control tools can help the practitioner navigate the difficult decisions in choosing the final equating function. This book provides a valuable reference for several groups: (a) statisticians and psychometricians interested in the theory behind equating methods, in the use of model-based statistical methods for data smoothing, and in the evaluation of the equating results in applied work; (b) practitioners who need to equate tests, including those with these responsibilities in testing companies, state testing agencies, and school districts; and (c) instructors in psychometric, measurement, and psychology programs. Dr. Alina A. von Davier is a Strategic Advisor and a Director of Special Projects in Research and Development at Educational Testing Service (ETS). During her tenure at ETS, she has led an ETS Research Initiative called "Equating and Applied Psychometrics" and has directed the Global Psychometric Services Center. The center supports the psychometric work for all ETS international programs, including TOEFL iBT and TOEIC. She is a co-author of a book on the kernel method of test equating, an author of a book on hypotheses testing in regression models, and a guest co-editor for a special issue on population invariance of linking functions for the journal Applied Psychological Measurement.