Quantitative understanding of molecular astrophysics rests on a series of molecular physics theoretical concepts. This book provides a proper description of the theory, its breakthroughs and its shortcomings, and a comparison with experiments and observations. This will enable students and astrophysicists to take advantage of the theoretical tools available.

The book is divided into 3 parts, aiming at giving the reader an understanding of the roles of molecular observations, and the pathway towards a qualitative and quantitative understanding of molecular gases in astrophysics.

Part I describes molecular astrophysics as a natural science, with observations at its core. It is the most qualitative part of the book. It describes the regions of the Universe where cold molecules are to be found and observed. It shows examples that are drawn from several horizons, from extra-galactic observations to planetary sciences. It emphasizes the perfect adequacy of molecular observations and the physical conditions of cold tenuous matter.

Part II is a detailed description of the molecular science needed for the understanding of molecular physics. A sizeable part is devoted to spectroscopy, the basis of everything we know about the molecules. It continues with a description of molecular collisions, of all kinds.

Part III puts together the results of part II and the reality of astrophysical conditions. How to analyze a spectrum, what is LTE, what are the limitations, differences between the various kinds of observations. It will draw heavily on actual observations and link to several worked out simulations.