woo 
(w)
(w)v. wooed, woo·ing, woos
v.tr.
1. To seek the affection of (someone, especially a woman) with the intent to marry or begin a romantic relationship.
2. To gain the favor of (someone) or move (someone) to do something by entreaties or inducements: an ad campaign that wooed customers away from their usual brand.
v.intr.
To seek the romantic affection of someone, especially a woman.
[Middle English wowen, from Old English wōgian.]
wooer n.