For the battle of antietam what is lee's strategy in this battle? ?

Lee's strategy was to win

George McCellans mistake
Moving too slowly to exploit his advantage of being able to destroy Lee's divisions, after discovering that they were widely separated.
A Confederate spy in his camp had managed to alert Lee, who quickly concentrated his forces at Antietam Creek.

Lee's mistake
Lee was one of the finest natural campaigners the United States Military Academy ever produced. Apart from that, he was a disaster on horseback. The brief campaign known as the Seven Days was a protracted and useless slaughter of Confederate infantry. Thomas Jackson was bringing his Army of the Valley to Richmond, and was supposed to make coordinated attacks with the rest of Lee’s army. Lee provided no maps, and didn’t even send a guide to him until the third day. The guide was a young cavalryman who soon got into an argument with Jackson about whether he was going to Old Cold Harbor or New Cold Harbor. Jackson spent most of the seven days wandering around in woods and swamps with no idea where he was going. Jackson had had maps made of every square foot of ground he fought over in the Valley, so it must have been frustrating for him. However, he had a religious attitude toward subordination, so he never complained. The Seven Days ended at Malvern Hill, where Federal troops had dug in just below the summit. Hunt, the Federal artillery commander, set up 40 to 50 guns on the crest. Lee then launched a series of what were basically suicide attacks on that position. Confederate General Daniel Harvey Hill said "It wasn't war; it was murder." Lee had more than 20,000 killed that the South could ill-afford
.
Was the bloodiest battle of the war resulting in
25,000 casualties

geography was important because it was made up primarily of fields and hills. Much of the fighting was done on farmland. A huge part of the battle took place in a cornfield. However, there were (at the time, not so much now) forests, too. They are currently trying to grow the forests back.

Tactically, the battle was a draw, as McClellan failed to break through the Confederate defences or destoy a significant portion of their army.
Strategically, it was a Union victory, as shortly after the battle Lee retreated back into Virginia, thusabandoning his invasion of the North.

Forces engaged:

Confederate - 38,000
Union - 75,000

Casualties:

Confederate 10,318
Union 12,401

The general ratio of wounded to killed in Civil War battles was 3:1

Finally an effect of the battle was the Proclamation of Emancipation
And also the South Lost the chance to gain support from Britain and France

hope this helps