Just like in English, there are two forms of progression in German: comparative and superlative. We can use them to show superiority, inferiority, or equality. There are different constructions you can use to form each of these.
The Comparative
Rule 1: The comparative is the first form of progression and describes things that are not equal.
It is formed with a simple formula: adjective + er.
Remember that all adjectives, whether used in positive, comparative, or superlative form, need to agree with the noun in gender, number, and case.
Rule 2: Adjectives with one syllable often form the comparative with umlaut (ä,ö,ü), i.e. alt - älter.
Expressing Equality
Rule 3: When we want to compare similar traits of people or things, we use:
so + adjective or adverb + wie
The Superlative
Rule 4: The superlative describes a maximum form of progression. It is formed with one of the following constructions:
1. a definite article der/die/das + adjective + ste/n/m/r/s
2. am + adjective + sten
Rule 5: Adjectives with one syllable often form the superlative with umlaut.