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This report consists of two parts. The first part is a brief exposition ofclassical descriptive set theory. This part introduces some fundamentalconcepts, motivations and results from the classical theory and ends with asection on the important result of Addison that established the correspondencebetween classical and effective notions. The second part is about invariantdescriptive set theory. It consists of a brief introduction to notions relevantto this branch of descriptive set theory and then describes in details some ofthe relatively recent results concerning equivalence relations between Polishmetric spaces.

Aspects of Classical Descriptive Set Theory