The 4000 was introduced initially in the U.S. as a 1980 model to replace the aging Audi Fox. The initial offering was a 1.6L 4-cylinder with 4-speed manual transmission, both in two and four door versions. A two-door, 5-cylinder model was later offered, with a 5-speed (Designated as the 4000 5+5). 

In 1981 the displacement of the 4-cylinder was increased to 1.7L, and a 5-speed maunal transmission was made standard. The 5-speed models often carry the 4+E badge that signifies 4 normal speeds plus an economy gear. This was a wide ratio 5-speed box. A 5-cylinder model with automatic transmission was also added. The Audi Coupe was also introduced in 1981 with a 5-cylinder 
engine. 

In 1982 they added the "S" designation, and dropped the 5-cylinder models, I don't know of a good reason for the additional "S", except that perhaps Audi wanted to designate the additional standard features in the newer models. A diesel and turbo-diesel model was available in 1982 and 1983, but proved to be unpopular. 

In 1984 the 4-cylinder displacement was increased again to 1.8L (the GTI engine). Also, the 4000S quattro (with all wheel drive and a 5-cylinder engine) was also added. In 1985 all 4000/Coupe models received extensive styling changes in the front grille, lights, bumpers, trunk, and interior. The 1.8L engine had much higher compression ratios, and also received the knock-sensing ignition system. A close-ratio 5-speed transmission was standard. In 1986 the 4000CS was a special model to commemorate the 100th anniversary of the automobile, with additional standard features. The 4000S quattro was also re-named 4000CS quattro.

The 1987 model year was the last of the 4000s before the 80/90 series took over.