Palace of Stone picks up about six months after Princess Academy leaves off. Considering the events of the first book, Miri is a very different girl at the beginning of book two than she was at the beginning of book one. She still has the same spirit, the same fire, and in many ways the same self-doubts. But she also has a hope for a wider world, a vision for her village, and a knowledge of her own strength. She has learned that if something needs to be done, she can't wait around for someone else to do it.
It's this Miri that travels with the traders' wagons, five other academy girls, and Peder, down the mountain to their capital, Asland. There they find a world wider than their imaginings, a city teeming with people, buildings and castles, libraries, an ocean. But their wagon has barely stopped before they realize that all in the lowlands is not as idyllic as it appears. There are poor in the city as well as on the mountain, and the king is demanding more tributes than the people can pay. When Miri realizes that her own village may soon suffer the same extortion from the crown, her loyalties are quickly divided between the rising revolutionaries and her friends within the palace.
In a way, Palace of Stone serves as a kind of introduction to the revolutions in our own histories, drawing from images of the American and French revolutions, while ever being grounded in Miri's own world. She serves as a kind of filter through which the reader can grapple with the same questions. Questions of justice, the right and wrong power of a government, and the same right and wrong power of the mob. Ultimately, it is a reminder that behind every question of justice, power, right and wrong, there are individual people whose stories matter.
In a way, the stories of these two books are surprisingly similar. In both, Miri faces repeated circumstances where something is just unfair. In Princess Academy, though, it is clear what that fairness means. She is surrounded by twenty other girls about her own age who are directly affected by her choices. In Palace of Stone, Miri realizes that her choices can have a direct affect on an entire nation. At first, this thrills her. But the responsibilities that come with that kind of influence can be dangerous. She will understand it best when she sees the entire nation - the king and the shoeless alike - the way she saw the other girls at the academy. People she knows, understands, and with whom she shares a fate of either violence or peace.
In all other ways, though, these books are very different. You don't have to have read Princess Academy to read Palace of Stone - though I suspect some familiarity with the magic of the place would be helpful, especially in the story's later moments. It definitely helps in understanding Miri's homesickness, as the reader cannot help but fall in love with the rough, beautiful Mount Eskel in the first book. Wherever you are in your reading of Shannon Hale's canon, take a moment for this one. It's worth it.