Don't know if Tech's stadium is the oldest, but Grant Field is the oldest continually used playing field among "Div I" college teams. If I'm correct (going completely from memory here), the stadium arrived a few years after the field was dedicated. The original grandstands were built by students on a slope approximately where the current East Stands sit, however the front row seats were set back about 20 or 30 yards away from the east sideline, so the fans were somewhat removed from the action. The horseshoe-shaped concrete stadium came later and was built by students, engineers and convicts. The stands were about the same height all the way around (no upper decks), but sometime in the 1950s / '60s they began building the upper decks. I know that the West Stands were finished around 1966, complete with an upper deck and new lower deck seating built atop pilings only a few feet above the original concrete seats. The North Stands consisted of aluminum bleachers; the track for track & field events went completely around the entire playing field and underneath the North Stands, so during competitions, sprinters actually disappeared from view of the spectators for a few moments. Long jumping, high jumping, etc., occurred in the semicircular space behind the south end zone. Underneath the North Stands was the weight room, and clustered nearby was the original Tech gym and swimming pool. Over near the steam whistle at the north edge of the West Stands was the old team meeting room/film room in addition to a small rec center, complete with pinball machines. The team cafeteria was underneath the East Stands. They replaced the original grass surface of Grant Field with Astroturf sometime in the early '70s.
Sometime between '78 and '82, the state-of-the-art Edge Athletic Center was constructed in the space between the North bleachers and the East Stands. At the end of the 1985 football season, the venerable old horseshoe (South Stands) was demolished and replaced by the Wardlaw Center, a multipurpose meeting center as well as a luxury viewing area for games. At first, there was no provision for seating in the south end zone, and if you look at footage from the late '80s -early 2000s, you'll notice the opposing teams entering / leaving the field via a portal directly behind the south goal post. (Tech goal posts were white for many years before they were finally painted yellow). Prior to the 1989 season, the hard, faded green Astroturf surface was replaced with an AllPro (?) artificial surface, which looked better and was much kinder on the players. The new playing surface was a brilliant green while the end zones were yellow. This surface didn't last long, as Atlanta won the bid for the '96 olympic games and Grant Field was to play host to soccer events. After about a two-decade absence, the grass surface returned to the Flats, though the noticeable crown at midfield was almost completely flattened to make it suitable for soccer. Many small additions have been made in the 2000s, giving the stadium its current appearance.