La bibliotecaria mi mostra un romanzo di un autore che non conosco.

Bibliotecaria is a feminine singular noun meaning female librarian. The article la must agree with it in gender and number.

• la bibliotecaria = the female librarian
• il bibliotecario = the male librarian

So this sentence specifically tells you the librarian is a woman.

Here mi means to me or me in shows me.

The verb pattern is:

• mostrare qualcosa a qualcuno = to show something to someone

So:

• La bibliotecaria mostra un romanzo a me = The librarian shows a novel to me

But in normal Italian, a me is usually replaced by the indirect object pronoun mi:

• La bibliotecaria mi mostra un romanzo

Because short object pronouns like mi, ti, gli, le, ci, vi normally go before a conjugated verb.

So:

• mi mostra = shows me
• ti mostra = shows you
• ci mostra = shows us

This is standard Italian word order with these pronouns.

Mostra is the third-person singular present tense of mostrare.

The subject is la bibliotecaria, which is she, so the verb must be she shows:

• io mostro = I show
• tu mostri = you show
• lei mostra = she shows

So la bibliotecaria mi mostra literally matches the librarian shows me.

It can mean either, depending on context.

Italian often uses the simple present where English might use:

• shows
• is showing

So this sentence could mean:

• The librarian shows me a novel
• The librarian is showing me a novel

Both are possible. Context tells you which one is intended.

Un is the indefinite article, so it means a novel rather than the novel.

Use un when the thing is not already identified as a specific one. Use il when both speaker and listener know which one is meant.

• un romanzo = a novel
• il romanzo = the novel

Here the sentence introduces the book as new information, so un is natural.

Here di means something like by in English when talking about authorship.

So:

• un romanzo di un autore = a novel by an author

Italian commonly uses di for this idea:

• un libro di Calvino = a book by Calvino
• un film di Fellini = a film by Fellini

So di un autore does not mean ownership here; it means authorship.

Because autore is also a singular count noun, and it is also indefinite.

So the sentence is talking about:

• a novel
• by an author
• and that author is not identified specifically

That is why Italian uses un again:

• un romanzo di un autore

If it were a specific author, you might have something like:

• un romanzo dell’autore che non conosco bene

But here the author is just an author, not a specific named one.

Because che is the correct relative pronoun when it is the direct object of the verb.

Here the verb is conoscere qualcuno = to know someone. It takes a direct object with no preposition:

• conosco l’autore = I know the author

So the relative clause becomes:

• un autore che non conosco = an author that/who I do not know

You usually use cui after a preposition:

• l’autore di cui parlo = the author I’m talking about
• la persona a cui scrivo = the person I write to

It refers to autore.

So the structure is:

• un romanzo
• di un autore
• che non conosco

That means: a novel by an author whom I do not know.

In other words, I do not know the author, not I do not know the novel.

In standard Italian, non goes directly before the conjugated verb to make it negative.

So:

• conosco = I know
• non conosco = I do not know

Italian does not need an extra verb like English do. It simply puts non before the verb.

Because Italian often leaves out subject pronouns when they are already clear from the verb ending.

• conosco already means I know
• non conosco already means I do not know

You could say che io non conosco, but that sounds more emphatic or contrastive. In a normal sentence, leaving out io is more natural.

No. This is a very important distinction.

• conoscere = to know a person, place, or thing; to be acquainted/familiar with
• sapere = to know a fact, or to know how to do something

Examples:

• Conosco quell’autore. = I know that author.
• So chi è quell’autore. = I know who that author is.
• So parlare italiano. = I know how to speak Italian.

Since the sentence is about knowing an author as a person, conoscere is the right verb.