Elds one page treatise on Gundam... Ok, it turned out to be 2.
Gundam follows our basic timeline up until modern day. From there terrorism goes on the rise, and starts effectively a global war on terror, or a third world war. This ends with all the worlds governments combining, doing all these amazing things, and stopping war, hunger, most diseases, etc. They also renew their space programs and figure out how to make fusion power work. This is by about 2050, mind you.
However, there's a problem. The Earth gets overpopulated and overpolluted. The solution ends up being to emigrate large groups of people to space. The Earth Federation spends a good hundred years building space colonies in seven different bunches, called "sides", most orbiting the Earth at the same distance as the moon (though 2 of them orbit the moon, I believe. Side 4 is also closer to Earth). They also figure out that Jupiter contains a sort of new energy source that can be used in the fusion reactors, called Helium 3. It's found out by a Professor Minovski, so it's dubbed the Minovski particle. Later in our story, it's found out that the Minovski particle can also be used to make beam weaponry and jam radar extremely effectively, which basically turns futuristic space fighting into WWII dogfights with giant robots and beam guns (WOO!)
Anyway, they build space colonies on the 7 sides, and a few around Jupiter, and some in the Asteroid Belt. A small percentage of people go to Jupiter and the Belt to mine, and though these people are important in other Gundam stories, they're not very important in this one (you may see a Jupiter supply fleet some time, but that's about it.) People start colonizing, and after about a hundred years of this, stop thinking of themself as Earthlings, or Earthnoids in this universe, and more as Spacenoids. They resent having to do things like pay taxes to the EF, and want to be self-sufficient. Oh! While I'm there, they make cities on the moon, too.
So along comes this guy called Zeon Zum Daikun. He is part of Side 3, and organizes Side 3 into the Republic of Zeon, and breaks away from the Earth Sphere. The EF does a trade blockade for this and doesn't allow anybody to travel to or from Side 3 except for military and political personell, and this inflames not only the Side 3 Spacenoids, but many others. The general idea becomes "EF SUCKS!" to a lot of people. Unfortunately, at this time, Daikun is assassinated by his second in command, Degwin Sodo Zabi. REALLY unfortunately, Degwin is a closet Nazi and has these ideas about the master race and all this stuff. Even MORE unfortunately, his eldest son Ghiren really does most of the work from here on, and he's twice the Nazi his daddy is. The show goes very far to paint the Ghiren = Hitler picture. They even have his dad call him Hitler.
Now, the Republic of Zeon is organized into the Duchy of Zeon, negotiations cease, and both sides start a military buildup by about 30 years. Unfortunately for the EF, professor Minovski lives on Side 3, and with his help the Zeon make a military that's ten years more advanced than the Earth Federations, which is 10 times larger. The Zeon include mobile suits and more advanced warships, and when the fighting starts, they wipe the floor with the EF for several months.
Now, I'd just like to say that not everybody in Zeon is a nazi. It's mostly just Ghiren and his buddies. But Ghiren and his buddies make up the core of the Zeon power structure, and thusly the entire Duchy takes on a Nazi'ish look. Most Duchy soldiers are idealists who just think their colonies should be seperate from the EF, they'd rather resolve things peacefully. The EF brass is really no better, it's mostly stuck up, rich politicians and old Admirals who couldn't be convinced they were wrong if you did so with a large metal pipe. The grunt soldiers of their forces are, however, probably just as much idealists, and think they're right. So you can't really look at Gundam from a position of right and wrong, or good and evil.
Back to our story. One other side also rebelled from the EF, Side 6. The Zeon helped them out and they won, and formed the Riah Republic. Riah is strictly neutral in every way towards the war, and has very, very precious little military power, but it should be noted that its citizens are spacenoids, and as such Riah does tend to see more towards the Zeon side of things.
Eventually, actually in January of UC 0079 (The era was changed to Universal Century when the first colony became populated by average people. Workers had been living in them for 50 years prior. I think we're in like... AD 2300 and some. Vlad knows the exact figure) war breaks out. Mobile suits are the main weapon of the Zeeks, and fighters and warships the main weapons of the Federation. Mobile suits btw are like 15 meter tall humanoid fighting machines, designed because they work well for combat in space. Later it was found out through field use that they were better than tanks and planes on land, but mobile suits were never very able to fly, plus they're really big, and for the entire war tanks and planes made a big difference in the land battle. Anyway, the thing is, most of the fighting was done around the colonies, and both sides used nuclear weapons. In the first few months of the conflict, something like 8 billian civilians died. The Zeon, with their better technology and tactics, overwhelmed the EF and nearly completely won the space war (the only space base the EF had left was Luna II, their defensive asteroid orbiting Earth. Zeeks do raids there a lot, but they've as of yet not been able to defeat the place.) and also won about 2/3rds of the Earth. Eventually a treaty was signed called the Antarctic Treaty, and weapons of mass destruction were outlawed, and there was also a one month armistice, in which time the EF worked frantically to build a mobile suit program.
One other thing of note - There was one mission called Operation British, where the Zeon dropped a depopulated colony on Australia, causing a crater that destroyed a corner of said continent, and turning most of the rest into a desert.
So now we're in the last half of the war. The Federation has a mobile suit program, and it is frankly better than the Zeons. They have improved armor, weapons and speed over the average Zeon MS, but the main two problems are that the Federation still has very little territory of its own, and it has just started making mobile suits. Pilots are learning as fast as the technicians, and there aren't many Feddie MS, and fewer experienced pilots.
The final note about Gundam is on Newtypes. It was discovered by the Zeon that at this time humans are at a new stage of evolution, and that that speeds up if you emigrate to space (in Ghirens eyes, the MASTER RACE! Mwa ha ha). Anyway, these people are very few, but exhibit limited psychic abilities. At low levels they may have an increased reaction time, and every once in a while have some sort of vision or something, but they can train their abilities, and powerful newtypes can read minds, speak to people telepathically, things like that. Extremely powerful newtypes have even been known to predict the future, float, visit people in their dreams from far away, or even instill limited newtype abilities in others for a period of time. The EF is just realizing that these people exist, but the Zeon have a full program for making them useful in the military, though it's a fledgeling program at best.
Anyway, that's about all you need to know. If you want to know more, I can give you many a rant, and so can Vlad. But he tends to be blunt, annoying, and talks at least twice as much as I do. But he also probably knows more about Gundam than I do. So, I guess you can pick your poison ^_^.