Okay, just to make clear of the time-line here (there might be some who are confused a bit)....
1. Rosecrans pushes Bragg out of middle-Tennesee in the Tulahoma campaign, ending July 3, 1863 (Rosecrans is upstaged by both Vicksburg and Gettysburg victories, he grumbled about how his success with very few casualties was under-appreciated). Bragg retreats to Chattanooga, holding only a tiny corner of S.E. Tennessee. Burnside moves down from Cincinnati with two corps from the Army of the Ohio, flanks the Cuumberland Gap, takes Knoxville from Confederate Gen. Simon Bolivar Buchner in August 1864, and starts to clear out Confederate in the mountains and valleys of E. Tennessee.
2. Rosecrans is urged to take Chattanooga by Halleck, and Burnside is pushed to move South to support Rosecrans. Burnside is in no hurry, he wants to make sure he can hold E. Tennessee with it's poor road network. Likewise, Rosecrans is spending time reconstructing and re-gauging railroads to bring supplies south to the Tennessee River in northern Alabama prior to opening the campaign against Chattanooga. Halleck is frustrated with both of them.
3. Finally, beginning on August 29, 1863, Rosecrans crosses the Tennessee at Bridgeport. A few scattered pickets dissapear, and he has three days to cross the river with his supply chains unmolested. Bragg remains in Chattanooga, frustrated by inadequate cavalry scouting, the lack of supplies, and the number of desertions (many are temporary).
4. Rosecrans spends several days traveling a short distance north-eastward but succeeds in crossing several mountain ridges with little opposition, the last one being the long tail of Lookout Mountain. Bragg is distracted (as intended by Rosecrans) by Wheeler's brigade and an artillary battery showing up to the north-east of the city, which lobs a few shells into town. Bragg thinks it is the beginning of the main effort, but Wheeler's forces are only a diversion, the main effort is already crossing Lookout Mountain at several passes south of Chattanooga and stradling the mountain along it's circumferance.
5. Bragg finally realizes he's about to get cut off in Chattanooga, so his soldiers start marching South. He almost gets Negley's division hemmed in at McLemore's Cove, but poor coordination among the division commanders allows Negley to escape back up the mountain. Rosecrans slows down, takes Lookout Mountain and then Chattanooga, before pursuing further.
6. Rosecrans moves South, believing Bragg to be retreating in disorder. But Bragg has decided to turn back north, and cut off the rear of Rosecrans from the front of his army, re-taking Chattanooga and cutting Rosecrans off from supply and reinforcement from Nashville. After a delay, Rosecrans realizes Bragg is moving north again. It's a race at this point, to see who can turn who's flank. It's essentially a tie - Bragg manages to cross the Chickamaugua creek, but instead of having a clear path around Rosecran's right flank he's managed to stumble upon Rosecran's extreme left flank. Both sides fight in the woods between Chickamauga Creek and Lafayette Road and jockey for position, with Rosecrans and Bragg both throwing in men as soon as they come onto the field. Eventually Thomas settles on a heavily fortified "fishhook" position just east of Lafayette Road, with other forces more or less taking opposite sides of the Road. There's lots of fighting on the northern flank of both armies as both try to seize the flanks. A good portion of Longstreet's two divisions are fed into the existing Confederate lines as they arrive on the field. Longstreet himself, having remained in Atlanta to arrange transportation for a bit longer, doesn't arrive until the end of the day, and doesn't find Bragg's heardquarters until around midnight - at which point he is told he will lead half of Bragg's army in the next day's battle, scheduled to commence at first dawn.
7. The next day (Sept. 20th) is the second day of the Battle of Chickamaugua. I wont' go into the details - the Union right holds most of the day, but the center is broken by Longstreet's charge. Thomas ends up defending Horseshoe Ridge and Snodgrass Hill while the rest of the army retreats back to Chattanooga, Thomas position in the "fishhook" disintegrates when it attempts to disengage right at the moment of a Confederate attack, but darkness prevents the Confederates from exploiting this advantage. Thomas' rear guard mostly gets away.
8. Rosecrans escapes to Chattanooga where, he explains, he is "organizing defenses". Dana, who is Halleck's spy in Rosecrans' army, is less complimentary. Soon Rosecrans is dismissed, replaced by Thomas. Confederate forces hold positions south and east of the city, Lookout Mountain, Lookout Valley, and Missionary Ridge. Supplies can be brought in only through a poor road over what is now known as Signal Mountain. But the Confederates are starving, the only areas from which they are allowed to take supplies are behind Union lines, the rich produce from Georgia and Alabama are designated for the ANV. Longstreet is convinced that Union reinforcements would soon be arriving, he argued for several plans to attack them while they were en-route, catching them before they could combine together. Bragg dithers, ignoring Longstreets' arguments. Finally a round-robing petition to remove Bragg and replace him with Longstreet makes it's way to Richmond, Davis comes to Chattanooga to try to resolve disputes within the AoT high command and put aside differences between his old buddies Bragg and "Bishop" Polk. He doesn't succeed. Bragg offers to step down if Davis thinks it would help. Davis offers Longstreet the job, but Longstreet refuses - he might have been able to do something with the AoP earlier, but now it's too late, he doesn't want to simp[ly preside over it's defeat after the available options have been allowed to be squandered away. Davis refuses to reward Polk by giving him command after pushing aside the existing commander, that would have set a bad precedent. So Bragg remains in command, Polk gets transferred, Longstreet is giving a long line from Lookout Mountain all the way to Bridgeport to guard with only a couple of divisions (less casualties from Chickamauga). Davis encourages Bragg to consider Longstreet's proposals, but no decisions are announced.
9. Grant is put in overall command of the relief effort. Burnside is ordered south from Knoxville to put pressure on the Confederate right flank at Chattanooga, Thomas remains at Chattanooga where the "cracker line" is reopened, Sherman works his way east over the Cumberland Mountains with a plan to cross the Tennessee just up-river from Chattanooga and fall upon the Confederate right flank and rear at Missionary Ridge, and Hooker is brought from the AoP in a circulor route through Kentucky, Nashville, Bridgebort, Alabama and then east toward Lookout Mountain.
10. Bragg has another falling-out with Forrest, and gives Wheeler most of Forest's men. Bragg then sends Wheeler on a raid into the Cumberland Plateau and as far east as McMinnville, Tennessee. It's about two weeks before Wheeler's men are back across the Tennessee River at Muscle Shoals, croosing at Oct. 9th, 1863.
10. Longstreet informs Bragg that Hooker's army has crossed the Tennessee and is on it's way toward Lookout Mountain. Bragg argues with him. Ultimately they have a meeting on top of Lookout Mountain about Oct. 28th, just in time to see Union troops marching in the valley at the base of the mountain. A plan is formed for a night attack at Wauhatchee, Bragg promises to send another division to assist in the attack, but then cancels those orders without informing Longstreet. After some confusion over the missing division, the attack proceeds at midnight, but fails. Union troops control the base of Lookout Mountain from the Tennesssee River southward down the long ridge and several passes over the mountain.
11. Hooker attacks Lookout Mountain like you would peel and apple, moving along a trail from the western side of the mountain up along it's circumference to a prominenent house at the top of the slope, before the walls become vertical columns of granite. Longstreet has to keep most of his men atop the mountain in expectation of an attack along the top of the ridge, the handful on the trail can't contain Hooker's men forever. Once Hooker is successful, Lookout Mountain becomes untenable as any further movement along the flank cuts off the mountain from retreat, re-supply, or reinforcement. Lookout Mountain is abandoned to Hooker's army.
12. Now, finally, Bragg decides is a good time to take care of the "un-unified" portions of Grant's army, and orders Longstreet with his two division of ANV troops plus a good portion of Wheeler's men to cut Burnside off before he can retreat back to Knoxville. Longstreet marches his men to Tyner Station where he waits two days for the trains to take him north so he can get ahead of Burnside. When Longstreet complains that the trains aren't available, Bragg responds by arguing that Longstreet should have handled those details himself (Longstreet had no authority to order trains moved anywhere).
13. Grant takes Orchard Knob (now the National Cemetary), a good place for artillary and command viewpoints. The Chattanooga front is moved forward halfway to Missionary Ridge. Sherman crosses the Tennessee River via pontoon bridge, but ends up on the wrong hill (he thinks he's on Missionary Ridge, but he's on Tunnell Hill just to the North. Bragg now has second thoughts about sending Longstreet away, he trys to recall Longstreet but is too late.
14. Grant's plans are for Thomas to demonstrate against Bragg in the center of Missionary Ridge and Hooker to threaten from the South, while the main effort would be from Sherman in the North. The plan doesn't work too well, Sherman gets stuck trying to cross the ravine between Tunnell Hill and Missionary Ridge, Clebourne's troops repell his assaults on the north. But Thomas men carry the center of the ridge (details are for another post), while Hooker's men cut through Confederate defenses at Rosseville Gap and start moving up behind Confederate forces to their rear (arguably placing them within yards of my old home in East Ridge, Tennessee). The Confederate line collapses, and the Confederates retreat to Dalton, Georgia.
15. Meanwhile, Longstreet is trying to out-pace Burnside, without success. Burnside is playing his role beautifully, keeping just outside Longstreet's reach and luring Longstreet further north while the bulk of the fighting is being conducted in Chattanooga to the south. Eventually Burnside reaches the Knoxville fortifications, and Longstreet learns that his maps are wrong. Longstreet's hopes to beseige Knoxville are defeated by an open supply route on the opposite side of the city. . He decides to try to break the defenses by attacking Ft. Sanders, on the hill to the south-west of the city. The engineer in charge has done a masterful job, making almost verticle walls of mud & dirt with water poured down them so that overnight they turn into layers of thick ice. An entrenchments in the front makes the barrier higher, and plank boards upon which pickects cross give the impression that it's a ditch only a couple of feet deep, but in reality it's four feet deep, adding to the eight-foot walls making them a total of twelve feet high. Telegraph wires are wrapped around tree stumps and bushes at ankle and knee level so as to trip and entagle the attacker.
16. Longstreet's attack on Ft. Sanders begins at dawn on Nov. 1863, the Confederates make their way through the obsticles to get stuck in the ditch below the fort wall. They can't do anything but shoot at someone who sticks there head out above them. There's no way to climb the wall, there's no way to retreat (the cannon fire upon the retreat would have been more dangerous than during the attack). And once Union artillarymen started lighting fuses and dropping the balls upon them, they couldn't stay where they were. Longstreet recalls the attack after twenty minutes, many lost their lives on the return run, about 200 had to surrender. Then Bragg receives messages indicating a disaster at Chattanooga.
17. Bragg orders Longstreet to send the cavalry to re-join Bragg. But Sherman's men block the way to the north, so Longstreet declines. He no longer has the time to besiege Knoxville if Union forces are free to pursue him northward. There's also little reason to hold the head of the Valley if the bottom is bottled up. So Longstreet drifts off to the north-east to spend an uncomfortable winter near Morristown, Tennessee, the next spring they work their way northward back to northern Virginia to join the ANV.
Bringing the