Translation:The woman reads the menu at the restaurant.
Because "the restaurant menu" is implicitly possessive: "the restaurant's menu." But the way it's given in the lesson, it's just someone doing a thing in a place, and we shouldn't assume the menu belongs to the restaurant. In another lesson, they might swap out "menu" for "book" and "restaurant" for "park" because they're testing our grammar as well as our vocabulary. In short, we should be simply translating these phases and sentences, not trying to interpret them for deeper meaning that may or may not be there.
Al can mean "to the"or "at the" depending on the sentence. Ai is the plural form of Al .. ex: "Io leggo al raggazzo" = I read TO THE boy. Ex: "Noi scriviamo ai ragazzi" = we write to the children. Another example for "AL" is this sentence above stating shes reading a menu AT THE restaurant because TO THE restaurant wouldnt be correct. To say shes reading the restaurant menu I believe is " lei legge il menu del restorante" but I havent gotten that far to say im correct on that part. Hoped I helped. Ciao amico !!
However, we who are learning by working through these lessons with no other reference must generalize from previous exposure. To wit: crema al cioccolato = chocolate cream, gelato al limone = lemon ice cream - thus menu al ristorante, which cannot reasonably mean restaurant menu on its own in English, must mean the restaurant's menu. A childs generalization type error. Incorrect but expected from previous exposure.
Well... Someone else pointed out in other sentence that in Italian "a" is in / at and "al" is the combination of "a" and "il". But it's not mentioned in the lesson, it's very confusing considering that "al" was used in a completely different way before. Searching for "al" in a dictionary doesn't help either. And besides "restaurant menu" makes absolute sense.
It should've been marked as a new word so people actually hover over the word to see what it means.
Which article you use depends on the gender and number of the noun, and what the next word begins with.
This is how the prepositions interact with the definite articles:
When I said it also depends on how the next word begins, I mean for example you would say "gli studenti" because "studenti" is masculine plural and begins with "st", but you would say "i miei studenti". It's still masculine plural, but "miei" begins with "m".