1.woo: [wu:]
Eventually he wearied of wooing fame and fortune.
他终于对追名逐利感到厌倦了。
He is trying to woo my sister.
他试图向我姐姐求婚。
2.run/go after: 追赶,追踪;追逐(对象等)
He's always running after women.
他老是在追女人。
3.pursue: 追求;向...求爱
She pursued the goal of perfection in her art.
她的目标是追求艺术上的完美境界。
衍生出来的有in pursuit of
4.court sb.
He has been courting Jane for six months.
他追求简已六个月之久。
seek :seek for
aspire: to aspire after
crave:crave for/after
chase:to chase
还有一个，直接用be after