Early Ideas about Comets -- Statistics of Cometary Orbits and Magnitudes -- The Understanding of Their Physical Nature -- Dynamics of LP Comets Entering the Inner Planetary Region -- The Oort Cloud -- The Flux of New Comets: Quiescent and Excited Stages -- The Jupiter Family -- The Trans-Neptunian Belt -- Physical End States of Comets -- Leftovers of the Solar System Formation -- Comets and Life.The book covers the most recent ideas about the nature and dynamics of comets, including a thorough discussion on Oort cloud dynamics which has not received due attention in other books on the subject. It also discusses the most relevant aspects of the physics and chemistry of comet nuclei, highlighting their importance as relics of the protoplanetary disk and, perhaps, as carriers of water and organics that permitted the development of life on Earth. The book contains several tables with useful data, and an ample bibliography covering the most recent work as well as some historical key contributions to the subject. It may be suitable as a textbook for graduate students with some basic knowledge of celestial mechanics and astrophysics, as well as a consult book for comet researchers, or researchers from other related fields willing to start working on comets, or get an updated view of the subject.