Rydberg states of H2+ will be studied by optical excitation of H2+, using a highly sensitive detection scheme that is based on the detection of slow protons from the dissociating molecule. Contrary to conventional Rydberg molecules, the H2+ Rydberg states are characterized by a core configuration (2 protons) that is strongly correlated with the quantum numbers of the Rydberg electron n and l, the sole electron in the molecule. The theoretical formulation of this three-particle system is in its foundations equivalent to that of the negative hydrogen atom. Experimental information on these states of H2+ is completely lacking at this point. These states will be explored for the first time with a unique experimental tool. A similar experimental approach will also be used to investigate rotationally quasi-bound states in the ground 1s sigmag state of H2+ and its isotopes by stimulated Raman scattering from the repulsive 2p sigmau state. Finally, the fast-neutral beam photodissociation technique will be utilized to study isotopes and configuration-interaction effects in the dissociation of neutral hydrogen to the H(1s) + H(2p) limit. The results of this work will aid the understanding of the structure and interactions of simple molecules.