It is widely recognized nowadays that conical intersections of molecular potential-energy surfaces play a key mechanistic role in the spectroscopy of polyatomic molecules, photochemistry and chemical kinetics. This book presents a systematic exposition of the current state of knowledge about conical intersections, which has been elaborated in research papers scattered throughout the chemical-physics literature. Section I of the book provides a comprehensive analysis of the electronic-structure aspects of conical intersections. Section II shows the importance of conical intersections in chemical-reaction dynamics and gives an overview of the computational techniques employed to describe the dynamics at conical intersections. Finally, Section III deals with the role of conical intersections for researchers in the fields of molecular electronic-structure theory, molecular spectroscopy, photochemistry and chemical-reaction dynamics.