to try hard to please someone, especially because you want something from them:
His campaign team have assiduously courted the media.
to behave in a way that makes danger etc more likely:
To have admitted this would have courted political disaster.
if a man and a woman are courting, they are having a romantic relationship and may get married:
That was back in the 1960s when we were courting.
if a man courts a woman, he spends time being nice to her because he hopes to marry her