Comparing two things is something you already do constantly in everyday speech — "this house is bigger than that one," or "the best one of all." German expresses the same ideas with three degrees of the adjective, and the key point is that the adjective itself changes shape in a fairly regular way each time, not just the word order around it.
The first degree is the positive (Positiv), the plain adjective you already know from A1: groß, schnell, alt. You use it when simply describing something, not comparing it to anything: Das Auto ist schnell.
The second degree is the comparative (Komparativ), used to compare exactly two things. The rule is simple: add -er to the end of the adjective, then add als ("than") before whatever you're comparing to: schnell → schneller als. Als works much like "than," and the word order mirrors it closely: Berlin ist größer als Köln.
Watch out: many short, one-syllable adjectives containing a, o, or u also add an Umlaut along with -er: groß→größer, alt→älter, jung→jünger, kalt→kälter. This vowel change carries no separate meaning — just memorize it together with the adjective.
The third degree is the superlative (Superlativ), used when comparing one thing against everything else (the best, the biggest, the most). When the adjective stands alone after sein with no noun following, it takes the form am + adjective + -sten: Im Sommer ist es am heißesten. But when the adjective comes directly before a noun (like "the highest mountain"), the pattern shifts to article + adjective + -ste: der höchste Berg — a second form of the same idea you'll explore further later.
For equality between two things, use so...wie instead of als: Er ist so alt wie ich. A very common mistake is mixing up als and wie: als is only for inequality (bigger than), wie only for equality (as...as) — never say so groß als.
Finally, a handful of adjectives are completely irregular and must simply be memorized: gut→besser→am besten, viel→mehr→am meisten, and especially gern→lieber→am liebsten, essential for talking about everyday preferences in food and hobbies.