You want to know the high points, not the details of every dayum battle ever fought by the Army.
When was the Army begun? The basics of the Revolution, including how hopelessly outclassed we were to fight the British toe-to-to. That changed when Von Steuben was put in charge of training. Yorktown. Cornwallis.
You could pretty much skip the War of 1812, from the Army point of view, except to say that the most famous battle, New Orleans, was fought after a peace was signed. Andrew Jackson.
WW1- the AEF, Blackjack Pershing, the Argonne.
WW2 - as much as you can read. It's all fascinating.
Vietnam - what can you say? The failure of the draft? A failure of leadership? (DC)
And on up to the present.
Good luck. History is great reading, even better than fiction.