The Army of Cumberland consisted of around 65,000 men and once they reached Chattanooga, they formed a semi-circle around the city. Rosecrans also deployed a few groups of smaller armies that were meant to be distractions for Bragg. Bragg was convinced that Rosecrans would attack from the north and decided to fortify the northern part of Chattanooga. Bragg saw a group of Union armies moving toward the city from the north and figured that he was correct to direct most of his attention there. Meanwhile, Rosecrans had his main army cross the Tennessee River and start pushing up through Georgia towards Chattanooga. Bragg learned of this plan and decided to withdraw his troops so that he was not cut off from Atlanta.
The Army of Tennessee was significantly smaller than that of the Army of Cumberland. The Confederates had only 40,000 men by the time they reached Chattanooga. Bragg requested to receive reinforcements from Joseph E. Johnson, whom had promised Bragg 11 brigades of infantry if he were attacked. Johnson did not actually have 11 brigades so instead he sent 6 brigades from W. H. T. Billy Walker and John Breckinridge.
The Union army crossed the Tennessee river in 3 separate places in their move to take Chattanooga. The crossing near Caperton's Ferry went miserable. The bridge that they had built collapsed and left part of their forces across the river for 3 days. They eventually made it across the river. Bragg was unsure of where all of the Union troops were at so he decided it was best to retreat from Chattanooga.
On September 19-20, 1863, the Army of Cumberland and the Army of Tennessee met in Chickamauga, GA. The battle had the second highest total casualty count in the war after the Battle of Gettysburg. The battle ended with a Union defeat that was the most significant defeat of the war in the Western Theater.