Likelihood serves as a unifying concept in both the theory and practice of statistical science. This is, in a sense, inevitable when probability models are used as a basis for inference. While the key ideas were set out in Fisher in 1922, and further developed throughout the 1930s and 40s, it was the ubiquity of the personal computer and the development of general-purpose software that made likelihood-based inference the method of choice in a wide variety of applications. This book provides an overview of the many “adjective”-likelihood functions that have been developed in various contexts, most of the likelihood-type inference functions current in the literature, while recognizing that a comprehensive treatment is not possible, as research on likelihood-based inference continues. This book is intended for readers with diverse backgrounds who have an interest in, or a need for, statistical methods in complex models. Some familiarity with likelihood-based inference and the main principles of estimation and hypothesis testing are assumed. The authors have used this text for graduate-level courses in inference and in specialized courses in likelihood-based inference.