to seek the favor, affection, or love of, esp. with a view to marriage.

to seek to win

to woo fame.

to invite (consequences, whether good or bad) by one's own action; court

to woo one's own destruction.

to seek to persuade (a person, group, etc.), as to do something; solicit; importune.

to make love to a woman; court

He went wooing.

to solicit favor or approval; entreat

Further attempts to woo proved useless.

noun

admirer , courter , suitor , swain