What part of speech is most?

It can be an adjective, an adverb, or a noun.

Adjective: Which of your friends has the most clothes?

'most' modifies 'clothes,' a noun.

Adverb: Your experience is most unusual.

'most' modifies 'unusual,' an adjective.

Noun: The most I can do is lend you ten bucks.

'most' is the subject of the verb 'is.'