What the national book in your country? That tome write possibly in the last century, that students need to study at school and that everyone knows, even though not many have actually read it?

Ours is Promessi Sposi (the bethroted). It's about a poor young couple in 17th century Italy that wants to get married, but the local Spanish nobleman who was the owner of the land has put his eyes on the girl and wants to kidnap her or something, so the couple gets separated and then shenanigans ensue.
The book was written in the early 19th century when Italy didn't existed and Austria was the owner of much of North Italy. Manzoni draw parallelism between Italy during 1600, a ruined shithole ruled by corrupted Spaniards, with the Italy of his day, ruled by corrupt Austrians. It's a good book, with some patriotism and well written, but the author was a massive religious lover and for today's standard it didn't age that well. The message of the book is basically " believe in the holy Providence and be a good person, and most things will solve themselves, and those who don't, well they weren't meant to be".