Led the Army of the Cumberland. Won the battle of Stones River against Bragg. Was later removed after being defeated at the battle of Chickamauga. William Rosecrans was an Ohioan, and after finishing school locally he went to West Point (class of 1842). He was posted to the Engineers (he'd finished fifth in his class) but a series of tedious peacetime assignments (teaching at West Point, various surveys, internal improvements) didn't fire his imagination. After a dozen years in the Army (and still only a 1st Lieutenant) he resigned to do something more profitable and interesting in business.
He returned to Ohio and worked as an architect and civil engineer, ran the Coal River Navigation Company, and founded the Preston Coal Oil Company. This was a kerosene company, and in 1859 he was burned in an industrial accident.
He returned to the army in 1861, first as Colonel of Ohio engineers, then Colonel of the 23rd Ohio Infantry, then Brigadier General of Volunteers. And all this was within three months of rejoining the colors. Rosecrans started out on McClellan's staff in western Virginia (he knew something of the region from the Coal River Navigation Company) and won a battle, but not the recognition, which McClellan snatched. When McClellan went to Washington Rosecrans inherited the whole district. After a couple more successful battles the egregious John Fremont was appointed over him.
That was enough, and he got himself moved out west. He served with Pope and Grant in western Tennessee. He fought at Iuka, then Corinth, and was promoted to replace Buell in command of the Army of the Cumberland. For a long time he just watched Braxton Bragg's Confederates, but he finally moved, and moved skillfully. He held on for victory at Murfreesboro (earning the Thanks of Congress), then maneuvered Bragg out of Tennessee and into Georgia almost without fighting in the Tullahoma Campaign.
With Bragg retreating, in September 1863 Rosecrans took Chattanooga, clinching Union control of central Tennessee by blocking Confederate access. But Rosecrans made his worst mistake. He thought he'd thrashed Bragg's forces, and started a pursuit, spreading his army to gain control of as much ground as possible. Instead the Confederates had reinforced, recognizing the importance of Chattanooga, and counter-attacked. The result was the battle of Chickamauga, and the eclipse of Rosecrans' reputation. He held the line on the first day, but made his mistake on the second: moving troops to cover a reported gap, he created a real one. Two-thirds of his army was routed, and George Thomas' stand (the rock of Chickamauga") probably saved everything.
Rosecrans was replaced the following month