The following guidelines apply to the comparative/superlative of most adverbs:
Adverbs of one syllable:
I can run faster than you. / I can run the fastest in my class.
She works harder than me. / She works the hardest of all students.
She ran more quickly than me. / Of all the students she ran the most quickly.
Informal forms of adverbs
In informal English it is common to hear the adjectival comparative/superlative form of two-syllable adverbs. For example with quickly:
She ran quicker than me.
She ran the quickest. (instead of more quickly – the most quickly)
Formal forms of of the pronouns with comparisons
Many educated English speakers prefer to use the subject form of Pronouns plus a verb rather than the object form without a verb in comparative sentences, especially in formal situations.
They say, for example: She ran more quickly than I did.
The alternative, omitting the verb as in the following examples, is considered to be even more formal and is avoided by most British English speakers: She ran more quickly than I.