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The evolution of the gaseous content of the universe can be traced by observing the changing number density per unit redshift of absorbers. Ly$-\alpha$ absorbers provide a unique sample that can be studied from $z_{\rm abs} \approx 0.0$ to $z_{\rm abs} >4.5$. The HST quasar absorption line survey of bright quasars provides a large and homogeneous data base for studying fundamental questions about the origin and evolution of gaseous systems in the Universe. The design, execution, and analysis of the survey will be reviewed. In addition, I will describe the ultimate goals of the survey as we enter the final stages of analyzing the data. The observational activity of the survey will be completed by the time of the AAS (the final observation is currently scheduled for 7 May 1995).
