Our proposal focuses on the preparation and writing of a book that will reflect a growing need for rigorous systematic presentations of classical and novel empirical likelihood (EL) approaches and their applications in Biomedicine and Health. With many examples, and data from biomedical studies, this book will explain newly advanced EL techniques applied to problems encountered in medical and epidemiological studies. A review of the modern scientific literature reveals the EL methodology is one of key components of highly efficient and robust non- and semi-parametric statistical tools in medical and epidemiological studies. The proposed book will cover basic/traditional EL techniques as well as novel approaches to performing non- and semi-parametric inferences that have been published in the literature, but have not published in a book format. The proposed book will also present efficient methods for constructing powerful distribution-free procedures to test composite hypotheses based on data that can be subject to different problems related to, e.g., missing values and limit of detections. The book will provide relevant software code for solving real data problems. The book material will be attractive and easily understandable to scientists who are new to the research area, including those who may not have a strong statistical background, and will also help attract statisticians interested in learning more about advanced topics. This book will also be aimed at biostatisticians who want to form a clear picture of various modern EL methods to extend and improve them. Drs. Vexler and Yu, PIs of this grant proposal, have been contacted by a well-known publisher that proved a great interest of receiving a book proposal related to the EL methods in Biomedicine and Health. The publisher pointed out that several independent experts in statistics, epidemiology and medicine indicated that the PIs have significantly contributed to the applied and theoretical EL methodology and the PIs are well positioned to write a book that will have an important place on the book lists of researchers in biomedical science. The authors of the proposed book apply for the grant to obtain an opportunity to write the book that requires time to be covered by the grant support. We shall collect, analyze and interpret relevant information published over the past 15 years in scientific journals, including the proposed book's authors' publications in Biometrics, Statistics in Medicine, Annals of Applied Statistics etc. Per each proposed method in the book, we will consider a large number of actual examples from medical and epidemiological studies to help the reader quickly learn novel empirical likelihood methods and apply them to real-life problems. We will aim to evaluate each described method in the contexts of theoretical and practical advantages and limitations. If fully successful, we believe that the proposed book has a great potential to be adopted as a primary manual regarding powerful statistical tools that change the practice of study planning for various clinical areas.