wooing

(noun) a man's courting of a woman; seeking the affections of a woman (usually with the hope of marriage). Synonyms: courtship, courting, suit. Example: "Its was a brief and intense courtship."

(verb) seek someone's favor. Synonyms: woo, court. Example: "China is wooing russia."

(verb) make amorous advances towards. Synonyms: woo, court, romance, solicit. Example: "John is courting mary."