Learn Italian: Marco è più grasso di Luca.

Unlike English, which often adds "-er" to the end of short words (like "fat" becoming "fatter"), Italian doesn't have an "-er" ending for adjectives. You always use più (more) plus the adjective. So, più grasso literally means "more fat", which is exactly how Italians say "fatter".

Why is the word di used here to mean "than"?

In Italian, when you compare two people, places, or things (like Marco and Luca) using an adjective (like grasso), you use di to mean "than". The basic recipe for comparing two nouns this way is più plus an adjective plus di.

If we were talking about a woman, for example Maria, how would this sentence change?

The adjective still has to match the subject of the sentence. Because Maria is feminine, the adjective grasso changes its ending to -a. The sentence would become Maria è più grassa di Luca.

How would I say that Marco is less fat than Luca?

To say "less... than", you simply swap più (more) with meno (less). The rest of the grammar works exactly the same way, so the sentence becomes Marco è meno grasso di Luca.