Which part of speech is "back" in “then she went back to her secretaire”? [duplicate]

Put the book back on the table.

I'm having trouble. I think it is a preposition.

First, and most important, asking what part of speech a particular word is tells you nothing about it, or about grammar, or about English. Nothing. Even if you get an answer. It's the wrong question.

Second, put back is a Phrasal Verb, and the back part is generally called a "particle". (See what I mean about telling you nothing?) The put part is called the "verb", which is also not terribly useful.

Phrasal verbs consist of a "verb" plus a "particle", which usually has the same form as a preposition, but doesn't have an object. Some linguists call it an "intransitive preposition", which means a preposition without an object. But the verb + particle unit acts together like a verb.

There are far more phrasal verbs than non-phrasal verbs in English, because every verb has several particles that it can occur with in a phrasal verb, with mostly unpredictable meanings.

It serves the function of controlling/modifying the verb put, so it is an adverb.

A preposition is a part of speech used to connect a noun or pronoun. Back is obviously not used in this way here. The only preposition here is on, as it connects the noun phrase the table.