¿Puedo llevarme este libro a casa?

Puedo is the 1st person singular form of poder in the present tense, so it means I can or am I allowed to.

In this sentence, ¿Puedo ... ? is a very common polite way to ask for permission:

• ¿Puedo entrar? = May I come in?
• ¿Puedo sentarme? = May I sit down?

So ¿Puedo llevarme este libro a casa? is literally something like Can I take this book home?

Because llevarse is being used here, not just llevar.

• llevar = to carry, to take
• llevarse = to take away, to take with oneself

The me means for myself / with me. It shows that the speaker wants to take the book away with them.

So:

• ¿Puedo llevar este libro...? could sound more like Can I carry this book...?
• ¿Puedo llevarme este libro...? clearly means Can I take this book away / take it with me?

This is very natural in Spanish when someone is asking to borrow or remove something from a place.

In Spanish, object and reflexive pronouns can be placed in two positions when there is a conjugated verb plus an infinitive:

• before the conjugated verb
• attached to the infinitive

So both of these are correct:

• ¿Puedo llevarme este libro a casa?
• ¿Me puedo llevar este libro a casa?

They mean the same thing. The version with llevarme is very common and natural.

Yes, absolutely.

Both are standard:

• ¿Puedo llevarme este libro a casa?
• ¿Me puedo llevar este libro a casa?

The difference is mainly word order, not meaning. In everyday speech, both are common.

Este means this.

It is a demonstrative adjective, used before a masculine singular noun:

• este libro = this book

Compare:

• este libro = this book
• esta revista = this magazine
• estos libros = these books
• estas revistas = these magazines

It has to agree with the noun, so because libro is masculine singular, you use este.

Spanish often makes a distinction between things that are:

• near the speaker → este
• near the listener / a bit farther away → ese
• far from both → aquel

So:

• este libro = this book
• ese libro = that book
• aquel libro = that book over there

In many everyday situations, este is used when the speaker is referring to a book they are holding, pointing to, or considering as the one right here.

In Spanish, a casa is a fixed, very common expression meaning home.

So:

• ir a casa = to go home
• llevar algo a casa = to take something home
• volver a casa = to return home

Using a la casa usually means to the house, meaning the physical building, not home in the everyday sense.

So:

• Me voy a casa. = I’m going home.
• Voy a la casa de Ana. = I’m going to Ana’s house.

Actually, in natural English we say take this book home, not to home. Spanish works similarly here.

The phrase a casa already expresses the destination home, so the sentence is natural as it is:

• llevar ... a casa = take ... home

This is just how both languages express this idea idiomatically.

Usually, llevar means to take / carry something away from where the speaker is or toward another place.

Very roughly:

• llevar = take
• traer = bring

So here, llevarme este libro a casa means the speaker wants to take the book away from the current place and go home with it.

Examples:

• Voy a llevar el libro a casa. = I’m going to take the book home.
• Voy a traer el libro mañana. = I’m going to bring the book tomorrow.

Yes. ¿Puedo ... ? is a normal and polite way to ask permission.

If you want to sound even softer or more formal, you could say:

• ¿Podría llevarme este libro a casa? = Could I take this book home?
• ¿Me puedo llevar este libro a casa, por favor? = Can I take this book home, please?

But the original sentence is already perfectly polite in most situations.

In Spain, coger is common and neutral, but it does not mean exactly the same thing here.

• coger = to take, pick up, grab
• llevarse = to take away with oneself

So:

• ¿Puedo coger este libro? = Can I take/pick up this book?
• ¿Puedo llevarme este libro a casa? = Can I take this book home?

If the idea is borrowing it or removing it from the place, llevarme is better.

A useful note: in much of Latin America, coger can have a vulgar meaning, but in Spain it is usually completely normal.

It is a yes/no question asking for permission.

Its basic structure is:

• ¿Puedo
  • infinitive phrase + ?

More specifically:

• ¿Puedo = Can I / May I
• llevarme = take with me / take away
• este libro = this book
• a casa = home

Spanish does not need a separate auxiliary like English do. The verb form itself does the job.

Spanish uses both:

• an opening question mark: ¿
• a closing question mark: ?

So questions are written like this:

• ¿Puedo llevarme este libro a casa?

This helps the reader know from the beginning that a question is coming.

The same happens with exclamations:

• ¡Qué bien!

Yes. In context, it usually implies taking the book home, often with the idea of borrowing it, not permanently keeping it.

The sentence itself does not explicitly say borrow, but in many real situations that is the obvious meaning.

If you wanted to say borrow more explicitly, you might hear:

• ¿Puedo llevarme este libro prestado? = Can I borrow this book / take this book on loan?

But the original sentence is very natural when asking if you may take a book home.