Who won the battle of Sharpsburg?

Answer 1

The Union troops under George McClellan.

It was a highly significant victory, which prevented Lee from invading Pennsylvania at a critical moment when the British were treating this as the test of Confederate viability, in advance of sending aid. Meanwhile it gave Lincoln the credibility to issue the Emancipation Proclamation, which gave the war a human-rights aspect, making it ethically impossible for the British to recognise the Confederacy.

It was not, however, regarded as a triumph of leadership on McClellan's part. He had had an extraordinary piece of luck, with a full set of Lee's orders falling into his hands (although a Confederate spy in the camp was able to alert Lee about this), but he moved too slowly to exploit his advantage to the full, and Lee's army was able to get home to Virginia in one piece.

McClellan was removed shortly afterwards.

Answer 2

The North, under McLellan, although he allowed Lee to escape back to Virginia.

Although the battle was tactically inconclusive, it had significance as enough of a victory to give President Abraham Lincoln the confidence to announce his Emancipation Proclamation,

Answer 3

aka Antietam