Ce livre est intéressant, je veux en lire un autre.

Livre is masculine singular and begins with a consonant, so French uses ce.

Use cet before a masculine singular noun that starts with a vowel or a silent h:

• cet ami
• cet homme

So:

• ce livre
• but cet article

French adjectives usually agree with the noun they describe.

Since livre is masculine singular, the adjective is also masculine singular:

• un livre intéressant

If the noun were feminine, you would use intéressante:

• une histoire intéressante

Here en is a pronoun that replaces livre(s) so you do not have to repeat the noun.

So:

• Je veux lire un autre livre
  becomes
• Je veux en lire un autre

In natural English, you usually do not translate en by itself. You translate the whole phrase:

• en lire un autre = read another one

It is the same spelling, but not the same function.

In this sentence, en is not the preposition meaning in. It is a pronoun.

So here, en means something like:

• of it
• of them
• one(s) of that kind

The exact English wording depends on the sentence.

Because en goes with the infinitive lire. It is the thing being read.

With vouloir + infinitive, pronouns usually go before the infinitive they belong to:

• Je veux le lire
• Je veux en lire un autre
• Je veux y aller

So en is before lire, not before veux.

Because livre is a singular count noun, and French normally needs a determiner before that kind of noun.

So French says:

• un autre livre = another book

At this level, it is best to think of un autre as the normal way to say another one.

Yes. That is the full version, and it is completely correct.

French often uses en to avoid repeating a noun that was just mentioned:

• Je veux lire un autre livre
• Je veux en lire un autre

Both are correct, but the version with en is more elegant and more natural when livre is already clear from context.

Because le and en do different jobs.

• Je veux le lire = I want to read it
  This means that specific book.

• Je veux en lire un autre = I want to read another one
  This means another book, not the same one.

So le points to a specific object, while en works when French is referring back to a noun with an idea like one, another, some, three, and so on.

Ce / cet / cette / ces can mean this or that, depending on context.

So ce livre may be translated as:

• this book
• that book

French often does not mark that distinction as clearly as English does, so context decides which translation sounds best.