Gromov-witten theory of projective bundles

In this dissertation, we will explore the Gromov-Witten theory of fibrations, especially with focus on projective bundles. It will be discussed from a few different perspectives and using different techniques. We hope our results might shed some light to the structure of the Gromov-Witten theory of fibrations, and hopefully offer some ideas for a few potential applications (e.g., the crepant transformation conjecture for ordinary flop and blow-up formulas).