No quiero ese libro; prefiero este.

Because Spanish often leaves out subject pronouns when they are not needed. The verb endings already show who is doing the action:

• quiero = I want
• prefiero = I prefer

So No quiero ese libro; prefiero este sounds natural. You could add yo for emphasis or contrast:

• Yo no quiero ese libro; prefiero este.
  = I don’t want that book; I prefer this one.

In normal Spanish negation, no goes directly before the conjugated verb:

• No quiero = I don’t want
• No prefiero = I don’t prefer

That is the standard pattern. Spanish does not usually use a separate word like English do in negatives.

Because ese libro is an inanimate object. Spanish uses the personal a mainly with specific people (and sometimes pets or personified beings), not with things.

Compare:

• No quiero a Juan. = I don’t want Juan.
• No quiero ese libro. = I don’t want that book.

So here a would be wrong.

Because preferir is a stem-changing verb. In the present tense, the e in the stem changes to ie in most forms:

• yo prefiero
• tú prefieres
• él/ella prefiere
• nosotros preferimos
• vosotros preferís
• ellos prefieren

So prefiero is the correct I prefer form.

They are both demonstratives, but they point to different things:

• este = this / this one
• ese = that / that one

In standard Spanish, including Spain:

• este usually refers to something near the speaker
• ese usually refers to something a bit farther away, or near the listener
• aquel refers to something farther away still

So the sentence means the speaker rejects that book and chooses this one.

Because Spanish can leave out the noun when it is already clear from context.

• ese libro = that book
• este = this one / this book

In the second part, libro is understood, so it does not need to be repeated. This is very common in Spanish.

You could also say:

• No quiero ese libro; prefiero este libro.

But repeating libro is less natural if the meaning is already obvious.

Because libro is a masculine singular noun, and este/ese agree with it.

• este libro = this book
• ese libro = that book

By contrast, esto and eso are neuter forms. They are used for unspecified things, ideas, or situations, not for a named noun like libro.

For example:

• ¿Qué es esto? = What is this?
• No quiero eso. = I don’t want that.

But once you say libro, you use este/ese, not esto/eso.

Because they must match libro, which is masculine singular.

Agreement works like this:

• masculine singular: este libro, ese libro
• feminine singular: esta revista, esa revista
• masculine plural: estos libros, esos libros
• feminine plural: estas revistas, esas revistas

So the form changes to match the noun’s gender and number.

Modern standard Spanish normally writes these demonstratives without accents:

• este, ese, aquel

Older texts sometimes use forms like éste or ése when they are pronouns, but current standard usage usually does not. So prefiero este is the normal modern spelling.

The semicolon links two closely related complete clauses:

• No quiero ese libro
• prefiero este

It shows a stronger break than a comma, but a closer connection than a full stop.

You could also write:

• No quiero ese libro. Prefiero este.

That is also correct. The semicolon just makes the relationship between the two ideas especially clear.