Quasi-adiabatic theory has applications across disciplines, from quantum computing and cosmology to materials science and atomic physics. This textbook provides, for the first time, a comprehensive introduction to quasi-adiabatic effects. In modern physics, the term "adiabatic" refers to the slow evolution limit. Nonadiabatic transitions are well understood also. Conversely, quasi-adiabatic theory pertains to a systematically developed theory revealing numerous time-dependent evolutions in physics that, while slow, are not genuinely adiabatic. It is rich in effects that can be understood even in models with complex many-body interactions. Examples from research in quantum computing, phase transitions, ultra-cold atoms, and quantum control are used throughout to illustrate these effects. Quasi-Adiabatic Effects: Introduction to Geometric Phases and Landau-Zener Transitions is aimed at students at graduate level and beyond, who are interested in quantum and classical mechanics, as well as complex analysis. The book seeks to fill a gap in the literature by providing an accessible introduction to both geometric phases and nonadiabatic transitions at a level sufficient to consider numerous applications. Some of the processes found here are discussed for the first time in a textbook format, including the Dykhne formula (Chapter 8) and multistate Landau-Zener theory (Chapter 11). This unique material makes Quasi-Adiabatic Effects a novel and important addition to the textbook literature of several topics encountered in modern research. Throughout the book, students will find discussions and complex analysis of these processes as well as problems to solve (with solutions also provided). The problems help refresh several elementary techniques which will become progressively useful throughout the chapters.