The mystery of the diffuse interstellar bands has been variously a curiosity, a co nundrum, and a nuisance for astronomers in the seven decades since the features were first noticed, but recently they have become a forefront issue in astrophysics. Ever since Paul Merrill, in a series of papers starting in 1934, pointed out the interstellar and unidentified nature of the bands, a Who's Who of twentieth century astronomers have tried their hands at solving the problem of identifying the carriers. Henry Norris Russell, Pol Swings, Otto Struve, Paul Ledoux, W. W. Morgan, Walter Adams, Jesse Greenstein, Lawrence Aller, and Gerhard Herzberg all briefly entered the stage, only to move on quickly to other problems where the chances for progress appeared more realistic. In more recent times a number of equally prominent scientists have pursued the bands, but generally only as a sideline to their real astronomical research. But in the past decade, and particularly in the past three years, the view of the search for the diffuse band absorbers as an interesting but perhaps quixotic quest has changed. Today there are several astronomers, as well as laboratory chemists, who are devoting substantial research time and resources to the problem and, as perhaps the most reliable indicator of the newly elevated status of research in this field, some research grants have now been awarded for the study of the bands.

The existence of subparsec structure in the cold diffuse interstellar medium has been the subject of some debate. After a review of the literature, we will present the first survey of Na I absorption lines seen toward binary stars, and so demonstrate that small scale structure is ubiquitous in the interstellar medium. We will explain details of the observations, reduction of the data and the various analyses which were applied to the data. We explore several models of the ISM and discuss them in the light of the data. Some thought is given to the possibility that some of the observed structure might be attributable to circumstellar gas, rather than interstellar gas. We conclude that the gas is most likely interstellar in nature. Finally, we outline several areas of study which could further the understanding of small scale structure in the interstellar medium and the physical processes which govern it.

The interstellar medium (ISM) is organized in different phases with distinctive temperatures, densities, and ionization. The complex interplay between the different phases of the ISM governs the physical and chemical evolution of galaxies. In this thesis, I focus on characterizing the neutral phases of the ISM, particularly the atomic hydrogen (HI) and diffuse molecular gas, using observations at radio wavelengths. To interpret and contextualize our observations, I also compare observational results to chemical models and multiphase ISM simulations. I present the largest sample of sensitive HI absorption ever constructed using data compiled from seven previous surveys. With this sample, I investigate correlations between the properties of the multi-phase HI and other key tracers of the interstellar environment. I provide constraints for the environments in which cold HI (the cold neutral medium, "CNM") and molecular gas are likely to form in the diffuse ISM. I also discuss observations of cold HI structures at physical scales

The interstellar medium (ISM) structure and dynamics are the result of the interplay between many physical processes such as turbulence, gravity, thermal processes, magnetic fields and cosmic rays which determine the modes of molecular cloud and star formation, and which in turn, define the global galactic properties. In this thesis, we have examined in detail the role played by thermal and gravitational instabilities in the ISM. We have shown that thermal instability (TI) is an effective agent of structure formation in the ISM which can compress diffuse interstellar gas by a factor of ~ 100, leading to the formation of dense molecular structures, which can, if dense enough, become gravitationally bound. However, TI, which operates on small scales (