Textbook in PDF format This book introduces modern series methods with a focus on applications in econometrics and statistics. It explores how new orthogonal series techniques can address challenges in model building and estimation, particularly for variables with unbounded support, nonparametric nonstationary data, and high-dimensional models. By extending traditional series methods, which are typically limited to variables with bounded supports, this book provides tools to tackle emerging problems in econometrics and statistics effectively. The book is organized into the following key parts. Part one provides the mathematical foundation for modern series methods, offering the theoretical background needed for their application. Part two introduces fundamental econometric concepts, including conditional expectations and regression models, within the context of modern series techniques. The last part examines advanced topics, such as the connections between series methods and generalized functions, and compares series methods with kernel methods, highlighting their respective strengths and use cases. With a balanced mix of theory and practical insights, this book is ideal for researchers, practitioners, and students looking to deepen their understanding of series methods and their applications in econometrics, statistics, and related fields