isso, the UC storyline incorporates several different Gundam series.

Start with Mobile Suit Gundam (the original Gundam series) in the year 0079
Then there's Gundam 0080, War in the Pocket. This is a short, only 6 episodes or so, and its actually one of my favorites, but its not that important for the UC storyline IMO.
Next is Gundam 0083. I didn't think this series was all that great, but it does an excellent job setting the scene for
Zeta Gundam. This is the motherloving kickass of all UC series. This series kicks tremendous amounts of ass.
Later they developed a movie that formally concludes the UC timeline called Char's Counterattack.

Technically the last UC Gundam series is F91, but I really don't count it... Couldn't stand the main character and never even finished it.

Also there is another short Gundam series set during the One Year War around the time of the first Gundam series. It's called 8th MS Team and is hella cool.