The construction of pX is described in an historical perspective. The theory of Boolean algebras is developed and used as a tool, primarily in a detailed investigation of 0 IN and p 3N\IN. The relationships between a space X and its "growth" PX\X are examined, including the non-homogeneity of $X\X, the cellularity of pX\X, and mappings of pX to PX\X. The Glicksberg product theorem which characterizes the products such that 0(x X ) = x (PX^) and related results are cc cc presented. Finally, the Stone-cech compactification is studied in a categorical context.

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