Just as in English, adjectives can be used to rate things, either by comparison (“Ruth is stranger than Richard“) or by outright superiority (“I am the greatest“). The former is called a comparative form, and the latter a superlative. These forms can be both regular (“happy, happier, happiest”) and irregular (“good, better, best”).
Latin comparatives are often used exactly like the English version: one thing is bigger or smaller or smellier than another. They can also suggest different shades of meaning. The comparative may mean more, but it can also mean rather, quite or pretty: laetior sum (“I’m pretty happy”). I am not comparing myself to sad people here, just suggesting that I am happier than usual.
Latin sometimes compares things in by using quam. Think of it as the English than, and the translation follows naturally. laetior sum quam tu means “I am happier than you.” Sometimes it uses the ablative case, which is not so familiar. But the meaning is identical. laetior sum te also means “I am happier than you.” In Lesson 10, Sulpicia asks Dulcius urbe quid est? “What is sweeter than the city?”
You will recognise comparatives easily. Just look for the characteristic -ior- combination, before the regular adjectival endings: fortior, pulchiorem etc.
As in English, the Latin superlative can indicate a judgement that something is absolutely the uppermost. “Disertissime Romuli nepotum”, says Catullus: O most learned of the descendants of Romulus. It can also be used emphatically, in a less literal way. “You’re the best!” isn’t the result of a survey of all available people. Neither is optima es.
Superlative forms are very recognisable because of their two consonants before regular adjectival endings: fortissimus-a-um, pulcherrimus-a-um.