The preposition di is one of the most common prepositions in the Italian language. Its basic definition, or rather, translation, is "of."

The title of a Yabla video about the famous Olivetti typewriter is La forza di un sogno. Here we can translate directly: "The strength of a dream."

Di = "of" in many cases.

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One way di is used is to show the purpose of something. In this case, we might have two nouns separated by di (of) After di, we don't need the article of the noun, when we are referring to purpose, although there may be exceptions to this.

A scuola di musica is the title of a series of videos about what the musical notes are called in Italian. If you like to play music, this might interest you.

In English, we can say "school of music" or we can say "music school." They mean the same thing. In Italian, we don't have the choice, except in some certain circumstances we won't worry about just now.

Just as we have la scuola di musica, where di means "of,"  we can guess the meaning of other, similar series of words connected by di.

un negozio di vino - wine shop

un museo di arte moderna - modern art museum or, museum of modern art

una casa di caccia - hunting lodge

uno studio di registrazione - recording studioun 

un professore di storia - history professor

In English, we can often use a noun as an adjective as in "wine shop," but in Italian we start with "shop" (negozio) and add di plus the kind of shop it is, also a noun.

Apostrophe for possession in English, but not in Italian

To show possession in English, we sometimes use the apostrophe, which we don't use in Italian. To translate in a parallel way, we have to turn the phrase around in English and imagine using "of," even though to use it sounds kind of awkward. 

For example, one Yabla video is called Battesimo di Philip.  In English, we could say, "Philip's baptism," but in Italian this form doesn't exist. We need di. In the caption itself, we've used the same formula for the English translation. It could have been: "my son Philip's baptism."

La... il battesimo di mio figlio Philip.

The... the baptism of my son Philip.

Caption 17, Adriano Battesimo di Philip - Part 1

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Sometimes di means "from"

One the first things we learn in a new language is to say where we're from, because inevitabilmente (inevitably), we'll be asked that. 

The basic question is: di dove sei  (where are you from)?  For this we use the verb  essere (to be).

"Di dove sei" è una domanda che io faccio per chiedere a una persona dov'è nata, l'origine.

Where are you from is a question I ask to ask a person where he was born, his origins.

Captions 9-10, Corso di italiano con Daniela Preposizioni in e a

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Note that di is at the beginning of the question. For the answer, we start with the verb (with the personal pronoun incorporated into it). Di by itself works for towns and cities. States, regions, and countries can be more complicated but we won't worry about that right now.

Sono di New York (I'm from New York).

Di  can mean "at" regarding time.

Di can mean "at" when we're talking about night and day, morning, afternoon, or evening:

eh... cucinando di notte, perché sennò di giorno fa caldo,

uh... cooking at night because otherwise it's too hot during the day,

Caption 68, Cucinare con le spezie di Franco Calafatti Introduzione

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Di  can mean "about" 

Racconta la storia di un burattino di legno

It tells the story of a wooden puppet

Caption 31, Adriano Pizzeria Pinocchio - Part 1

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We could say, "Pinocchio is a story about a wooden puppet."

There are other ways in which we use di, too many to list here. But we will close with a few common ways to say, "You're welcome" with di.

If you want to minimize what you did for someone, you can say:

Di niente (it was nothing).

Di nulla (it was nothing).

Non c'è di che (there's nothing [to thank me] for).

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