Trantor is the capital of the Galactic Empire. One massive city encompasses the planet, covering the surface "in the ever increasing complexities of man-made structures" (I.3.20). Everything and everyone are completely contained within this city's massive buildings, so much so that the population of Trantor rarely, if ever, sees the sky and stars. Sounds pretty awful, if you ask us.
But that's not all there is to it. Trantor is based on Rome at the peak of its power, right before the beginning of the slow collapse of the Roman Empire. Just like Rome, Trantor has spread itself too thin, claiming more planets than it can properly manage. It's also over-specialized as the sole seat of political power.
As Gaal puts it, this abundance of political power makes Trantor a great "prize" for other nations and power-hungry families (I.4.32). Also, since the entire planet is one big city, they can't grow crops to feed the population, which makes them depends on other planets to feed them.
Between the thinly-spread empire, the over-specialization of political power, and utter lack of raw materials, it must not have been hard for Seldon to predict Trantor's inevitable fall. Worse, the leaders are too busy being caught up in the hustle and bustle of city life to see the end coming—again, just like Rome. They don't know that their inevitable doom will come from the outside-in.
Like Trantor, the Foundation has its own historic parallel. In this case, the Foundation acts a lot like a monastery from Europe's medieval era.
Warning: history lesson in 3…2…1!
When the Roman Empire fell, Western Europe entered a period that we like to call the Dark Ages. As the name suggests, it wasn't the most pleasant of eras. (Although we should point out that plenty of other parts of the world were doing just fine. Hello, algebra.)
But in the areas that used to be the Roman Empire, you could set a clock to how often barbarian tribes fought and raided their neighbors. This meant that high culture and education—things like science, philosophy, and literature—weren't as high on the to-do list as, say, sword-sharpening and learning how to store ill-gotten gains.
Enter Christianity, which built monasteries all over Europe.
(Brain snack: at this point—we're talking after the Roman Empire fell in at the end of the 5th century C.E.—there was no Roman Catholic Church, just a Western and an Eastern tradition of the same One True Church. In 1054, the Church split into Roman Catholicism and Eastern Orthodox.)
Sure, the monasteries helped the Church maintain political and financial power in a region. But they also kept knowledge going. The monks copied famous works of literature, science, and philosophy in scriptoriums and maintained large libraries, like knowledge-fortresses. They also provided education for local boys who wanted to be priests or, you know, work a job that didn't require murder on your resume.
Okay, history lesson over. Let's get back to the book.
The Foundation symbolically acts like a monastery for Asimov's future history, only presumably without the celibacy. The first Foundation creates the Encyclopedia Galactica, a resource consisting of all the scientific and mathematic knowledge in the galaxy. Even when they discover that Seldon doesn't care if they complete the book or not, the Foundation kept on gathering and improving scientific knowledge, coming up with technology that even the once-great Galactic Empire did not have. (Hello, alchemy-machine!)
Also like the monasteries of the Dark Ages, the Foundation teaches members of the nearby planets how to use technology and position themselves as a religious hub in the process. This helps them consolidate power, so they become indispensable to the barbarian worlds. Very convenient.
The Four Kingdoms were once provinces of the Galactic Empire, but, as the Empire weakened, they broke free into independent Kingdoms. Historical parallel? You bet. The tribes in England and Germany that broke free of Rome as it weakened.
The Four Kingdoms lack the nuclear power and scientific savvy of the Foundation, so they rely on the Foundation to keep them up-to-date on all things tech. The Foundation is basically their galactic Apple Store.
But, like a bunch of iPhone addicts bent on the latest gadget, the Four Kingdoms are barbarous in nature. They tend to use violence and intimidation to get what they want. So, the Foundation has to use more subtle methods to prevent a full-on confrontation. Through political, religious, and economic manipulation, the Foundation keeps the Four Kingdoms in check, so one never becomes more powerful than the other.
Of course, this doesn't stop the rulers of the Four Kingdoms from trying to gain more power through violence and intimidation—like Wienis of Anacreon. But then again, look what happened that that guy.
Of the Four Kingdoms—Anacreon, Smyrno, Konom, and Daribow—only Anacreon actually makes an appearance.
Like the Four Kingdoms, Askone doesn't have tech. But they've caught on to the Foundation's trick of selling religion with their science and tech, so the planet's leaders have made trading in Foundation goods illegal. This law lands Gorov in jail and sets into motion the events of "The Traders."
Mallow visits Swienna briefly during "The Merchant Princes." Swienna is still a planet under the control of the Galactic Empire, even though it sits just at the edge of the territory. Devastated by failed rebellions, the planet is poor and weak—like some post-colonial nation in Africa, trying to get back on its feet.
Although we don't get much of Swienna in Foundation, the planet does make a return appearance in the sequel Foundation and Empire. So, if you're interested in what becomes of the planet—keep reading.