Nuclear molecules are analogous to ordinary electronic molecules. Valence nucleons are circling nuclear cores and thus bind them. They appear in collisions of nuclei on nuclei, and in fission and fusion processes. Here a lively field of research has developed over the past 20 years. Nuclear Molecules are the strongest deformed nuclear complexes and play an important role in nuclear structure (cluster) physics. They are also of considerable interest for the synthesis of elements in astrophysics (cosmology). Most of the various nuclear molecular phenomena are discussed.This book is the first monograph exclusively written to cover the theoretical aspects of nuclear molecular phenomena in heavy ion collisions. The experimental evidence is presented and confronted with theory.