Also look at:
Audi Coupe / Audi Quattro, The history of
Audi S2
Audi RS2
A very brief history
B1 (1972-1978)
The model debuted in Europe in 1972 as the 80 and in 1973 in the United States as the Fox. Based on VW Passat, it was available as either a 2dr or a 4dr sedan. It effectively took the place of several models that Audi had discontinued (the Audi 60/72/75/80/Super 90 series), and provided the company with a viable rival to the Opel Ascona and the Ford Taunus. Audi also offered a station wagon variant of the vehicle in some countries, although it was virtually identical to the European VW Passat wagon.
There was also a sporty version available: Audi 80 GTE. With its fuel-injected four cylinder engine, which became world famous in the VW Golf GTI Mk1, it was slower as the lighter Golf but was still a fast car for its time.
B2 (1978–1987)
Audi redesigned the 80 on the B2 platform in 1978. They continued to use the 80 nameplate in Europe, but began badging it as the 4000 in North America. The Audi 80/4000 was now further away from the close cousin VW Passat, a station wagon was no longer offered in any country.
The bodywork of the B2 Audi 80 was designed by Giorgetto Giugiaro. What we today would regard as nice, but edgy design, was back then called aerodynamically optimized.
Audi 90 was introduced in September 1984, it can be described as the luxury version of the Audi 80, with only five cyl. engines available. Audi had already used a similar strategy with 100/200 series since late 1970s.
The B2 platform proved to be both quite versatile and quite profitable; Audi spun Quattro, Sport Quattro and Coupe variants off of the B2 platform, which in the process helped to cement the company into the public eye after their four wheel drive Quattro system proved useful in various forms of racing.
B3 (1987-1992)
Audi again revised the 80, this time on the B3 platform and introducing a new aerodynamic look and a galvanized bodyshell. In addition, the 80 model name became the worldwide name for the car. Range of new gasoline and diesel 4-cylinder engines became available and the 5-cylinder Audi 90 continued as an upmarket variant of the standard model.
B4 (1991-1995)
The B3 got a facelift in 1991 and new platform designation, becoming the B4. In Europe, the 90 name was discontinued and all sedans were badged as 80, regardless of which engine they had. Audi of America went the opposite direction, and began selling the sedan as the 90 and the coupe as the 90 Coupe.
80-based Avant and Cabriolet models debuted on the B4 platform, meaning that Audi now had sedan, coupe, cabriolet and wagon variants of the 80 available to European customers.
The sport model of Audi 80 was called Audi S2, which was available as Coupe, Avant or as 4dr sedan. Latter is ultra-rare, with only 271 ever built.
The B4 platform was also used between 1994 and 1995 as the basis for Audi's RS2 super wagon, which was modified for them by Porsche.
The Coupe was discontinued in 1996 in Europe, and the Cabriolet model as late as 2000.
Sources: audistory.de, wikipedia.org