Abstract:  In this talk, I will first give a brief introduction to Batalin-Vilkovisky quantization as a mathematical theory describing the quantization of field theories with gauge symmetries. Then I will explain some of my works on the application of BV quantization in geometry and topology, including Fedosov quantization in symplectic and K\"ahler geometry, topological B-model in mirror symmetry and Rozansky-Witten invariant.