In this lesson you saw many more examples of prepositions (a, di and da) combining together with the definite article (il, la etc.) to form a single word. Most of these combinations are fairly intuitive. Note that when di combines with the definite article the i changes to an e: di + il = del, di + la = della etc.
The preposition di has a number of different uses in Italian.
One of the main uses is to express possession: il libro di Maria, Maria’s book, il fratello di Rosa, Rosa’s brother.
Many uses are the exact equivalent of the English word of: Una tazza di caffè, a cup of coffee, un pezzo di carta, a piece of paper.
A peculiar use of di which doesn’t have an equivalent in English is the so-called partitive construction. In this construction di combines with the definite article to mean some. Ho del pane, I have some bread, Compro dei libri, I buy some books.
Sometimes the only way to tell how di is being used is from the context: il piatto di cibo = the plate of food, but il piatto di Vincenzo = Vincenzo’s plate.