What war did Ulysses S. Grant bravely fight in?

Grant lead troops into numerous battles during the Civil War. Strictly speaking, he only commanded a specific Corp or Army prior to becoming Lieutenent General and General in Chief of the US Army. After that, he was responsible for all battles fought by US Army personnel, including Sherman's & Sheridan's battles (for example) even though he wasn't actually present near the battlefield. However as the top General he moved with the Army of the Potomac even though that Army was nominally commanded by Meade. Major Battles in the Western Theatre: Belmont, Henry, Donelson, Shiloh, Vicksburg campaign, Chattanooga Battles with the Army of the Potomac during the "Overland" or "Grand" campaign: Wilderness, Spotsylvania, Cold Harbor, Petersburg