This book introduces the authors' recently developed approach to inference: the inferential model (IM) framework. This logical framework for exact probabilistic inference does not require the user to input prior information. The book covers the foundational motivations for this new approach, the basic theory behind its calibration properties, many important applications, and new directions for research. It explores a new way of thinking compared to existing schools of thought on statistical inference and encourages readers to think carefully about the correct approach to scientific inference.