A study was conducted to demonstrate the formation of ultracold molecules through photoassociation. The process of photoassociation involved heteronuclear dimers, inelastic collisions, and interactions with ultrashort laser pulses. The photoassociation technique provided molecular samples with ultimate control over the internal states at phase-space densities, starting from a gas of atoms near or at quantum degeneracy. Photoassociation also involved the excitation of a bound molecular state from a continuum state of two freely scattering atoms. The cross section for photoassociation of a bound excited molecule from a free atomic pair tended to grow with increasing internuclear separation of the atoms due to two effects. The involved the possibility of finding another atom at a distance R scales as R 2, while the second effect involved the suppression of amplitude of the scattering wave function in regions where the chemical interaction of the two free atoms exceeded their thermal energy.