Learn French: Le chapeau de mon grand-père est rond.

In French, you cannot use an apostrophe 's' to show possession. Instead, you have to use de (of). So, "my grandfather's hat" literally becomes "the hat of my grandfather" (le chapeau de mon grand-père).

We are learning about prepositions like à côté de in this lesson. Is the de in this sentence doing the same thing?

In this sentence, de shows simple possession (the hat of my grandfather). In complex prepositions like à côté de, it connects the location phrase to the noun (the side of the house). It is the exact same word acting as a bridge in both cases!

Does the adjective rond describe the grandfather or the hat?

It describes the hat! The subject of the sentence is Le chapeau, which is masculine and singular, so rond is also masculine and singular. If the subject were a feminine object, like a table, it would be La table est ronde.

Why is there a hyphen in grand-père?

French uses a hyphen to connect the two words into a single compound noun meaning "grandfather". Literally "big father", it works similarly to the English prefix "grand-". For a grandmother, it becomes grand-mère.