Nuclear molecules are analogous to ordinary electronic molecules. Valence nucleons are circling nuclear cores and thus binding them. They appear in collisions of nuclei on nuclei, and in fission and fusion processes. Nuclear molecules are the strongest deformed nuclear complexes and play an important role in nuclear structure (cluster) physics. They are also of interest for the synthesis of elements in astrophysics (cosmology). Most of the various nuclear molecular phenomena are discussed. This book covers theoretical aspects of nuclear molecular phenomena in heavy ion collisions. The experimental evidence is presented and confronted with theory.