During the 1980-81 academic year the Department of Mathematics at the University of Connecticut had the privilege of being host to a Special Year in Analysis. Visitors joined us for periods ranging from a few days to the entire year. Most of them gave talks or series of talks on their recent research. These lecture notes are, roughly, the written versions of most of these expositions. The year's activities, and therefore these notes, focus on topics in Banach spaces, harmonic analysis, and probability, as well as the intern-actions between these areas; occasional contributions are only secondarily or tangentially in one or more of these areas, with primary emphases elsewhere in analysis.