Classifications and applications of symplectic fillings of Seifert fibered spaces over S²

This dissertation focuses on classifications and examples of symplectic fillings of Seifert fibered spaces over S² with a canonical contact structure. Broad results are obtained describing how such fillings arise. In large families of examples, explicit and complete classifications are given. Examples of such fillings can be used to produce symplectic cut-and-paste operations. These operations are strict generalizations of the rational blow-down operations, and their relations to the rational blow-down are discussed. Reinterpretations of these cut-and-paste operations as monodromy substitutions are also explored.