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Since their introduction in 1994, the Seiberg-Witten invariants have becomeone of the main tools used in 4-manifold theory. In this thesis, we will usethese invariants to identify sufficient conditions for a 3-manifold to fibreover a circle. Additionally, we will construct several examples of genus 1 and2 surface bundles and prove their total spaces are spin 4-manifolds.

Seiberg-Witten Invariants, Alexander Polynomials, and Fibred Classes