Splitting of logarithmic Gromov-Witten invariants under degeneration

In this dissertation, I study the theory of punctured Gromov-Witten invariants built by Abramovich, Chen, Gross and Siebert. I prove a splitting formula that reconstructs the logarithmic Gromov-Witten invariants of simple normal crossing varieties from the punctured Gromov-Witten invariants of their irreducible components, under the assumption of the gluing strata being toric varieties.