Quantum gravity is a highly complex and active area of research, and there isn't a single book that provides a comprehensive and universally accepted introduction to the subject. However, there are several books that can serve as good starting points, depending on your background and interests. Here are a few recommendations:
"A First Course in General Relativity" by Bernard Schutz: Before delving into quantum gravity, it's crucial to have a solid understanding of general relativity, as it forms the basis for many approaches to quantum gravity. This book provides a clear introduction to general relativity, suitable for beginners.
"Quantum Field Theory in a Nutshell" by A. Zee: Quantum field theory (QFT) is an essential framework in understanding the quantization of fields and particle interactions. This book introduces QFT and discusses its relevance to particle physics and gravity. It can provide a useful foundation for understanding quantum gravity.
"Quantum Gravity" by Carlo Rovelli: Rovelli is a renowned physicist and one of the leading researchers in loop quantum gravity. In this book, he provides an overview of different approaches to quantum gravity, including loop quantum gravity and string theory. It offers an accessible introduction to the subject.
"The Elegant Universe" by Brian Greene: Although not solely focused on quantum gravity, this book explores the concepts of string theory, which is one of the prominent approaches to quantum gravity. It provides a fascinating introduction to the fundamental ideas of string theory and its implications for our understanding of the universe.
"Quantum Gravity" edited by Claus Kiefer: This book is a compilation of chapters by various experts in the field, covering different aspects and approaches to quantum gravity. It offers a broad overview and allows you to explore different perspectives and ideas in the field.
Remember that quantum gravity is a complex and evolving field, and the understanding of the subject is still developing. It's recommended to have a solid foundation in general relativity, quantum mechanics, and quantum field theory before diving into quantum gravity. Additionally, keeping up with current research papers and articles can provide valuable insights into the latest developments in the field.