The book "Effective Action in Quantum Gravity" by I L Buchbinder, S D Odintsov, and I L Shapiro, published by Taylor & Francis in 1992, is a comprehensive treatise on the effective action in quantum gravity. The authors provide a detailed exploration of the fundamental aspects of quantum field theory and their application to gravitational theories. The book is divided into three main parts: 1. **Elements of Quantum Field Theory**: This part introduces the basic models of quantum field theory, including scalar, vector, antisymmetric second-rank tensor, symmetric second-rank tensor, and Dirac spinor fields. It covers the construction of field theory models, the Lagrangian formalism, and the effective action. The authors also discuss renormalization and renormalization group equations in curved space-time. 2. **Quantum Field Theory in Curved Space-Time and the Effective Action**: This part delves into the quantum theory of interacting fields in curved space-time, focusing on renormalization group methods. It includes discussions on renormalization in curved space-time, renormalization group equations, and the asymptotic behavior of effective couplings. The authors also explore the renormalization group method in curved space-time with torsion and the effective action in curved space-time. 3. **Selected Problems of Quantum Gravity**: This part addresses specific problems in quantum gravity, such as higher-derivative quantum gravity, asymptotically free models of grand unification with quantum \(R^2\) gravity, and effective action in multidimensional quantum gravity. It also covers the quantum properties of torus compactified membranes and the vacuum energy in torus compactified strings. The book is intended for researchers and graduate students in high-energy theoretical physics and gravitational theory. It provides a thorough treatment of the effective action in quantum gravity, making it a valuable resource for those interested in the subject.The book "Effective Action in Quantum Gravity" by I L Buchbinder, S D Odintsov, and I L Shapiro, published by Taylor & Francis in 1992, is a comprehensive treatise on the effective action in quantum gravity. The authors provide a detailed exploration of the fundamental aspects of quantum field theory and their application to gravitational theories. The book is divided into three main parts: 1. **Elements of Quantum Field Theory**: This part introduces the basic models of quantum field theory, including scalar, vector, antisymmetric second-rank tensor, symmetric second-rank tensor, and Dirac spinor fields. It covers the construction of field theory models, the Lagrangian formalism, and the effective action. The authors also discuss renormalization and renormalization group equations in curved space-time. 2. **Quantum Field Theory in Curved Space-Time and the Effective Action**: This part delves into the quantum theory of interacting fields in curved space-time, focusing on renormalization group methods. It includes discussions on renormalization in curved space-time, renormalization group equations, and the asymptotic behavior of effective couplings. The authors also explore the renormalization group method in curved space-time with torsion and the effective action in curved space-time. 3. **Selected Problems of Quantum Gravity**: This part addresses specific problems in quantum gravity, such as higher-derivative quantum gravity, asymptotically free models of grand unification with quantum \(R^2\) gravity, and effective action in multidimensional quantum gravity. It also covers the quantum properties of torus compactified membranes and the vacuum energy in torus compactified strings. The book is intended for researchers and graduate students in high-energy theoretical physics and gravitational theory. It provides a thorough treatment of the effective action in quantum gravity, making it a valuable resource for those interested in the subject.