Quiero volver a la biblioteca mañana.

In Spanish, when one verb follows another and the first one is a verb like querer, poder, necesitar, saber (meaning to know how), etc., the second verb normally stays in the infinitive.

• Quiero volver literally means I want to return.
• Quiero is already conjugated for yo (I), so volver must stay in its base form (infinitive).

You cannot conjugate both verbs like ✗ Quiero vuelvo. Only the first verb (quiero) is conjugated; the second (volver) stays in the infinitive.

Quiero is:

• Verb: querer
• Person: 1st person singular (yo)
• Tense: present indicative
• Meaning: I want

Spanish usually drops subject pronouns when the verb ending already shows who the subject is. So:

• Quiero volver a la biblioteca mañana.
  and
• Yo quiero volver a la biblioteca mañana.

mean the same thing. The version without yo is more natural in everyday speech unless you want to emphasize I (for example, Yo quiero volver, pero él no – I want to go back, but he doesn’t).

With verbs of movement such as ir, volver, venir, salir, etc., when you talk about going to a place, you normally use the preposition a:

• volver a la biblioteca = to return to the library
• ir al cine = to go to the cinema
• venir a casa = to come home / to the house

If you said ✗ volver la biblioteca, it would sound like to return the library (as an object), which is not the intended meaning. The a is essential to show direction toward a place.

Al is actually a + el:

• a + el = al (used with masculine singular nouns)
• a + la stays separate (used with feminine singular nouns)

Biblioteca is a feminine noun:

• la biblioteca = the library
  So you must say:

• a la biblioteca (to the library), not ✗ al biblioteca

Examples for comparison:

• al parque (a + el parque, masculine)
• a la playa (feminine, so you do not contract it)

In Spanish, when you talk about a specific place like the library, the cinema, the office, you normally use the definite article (el / la / los / las).

So a la biblioteca corresponds to to the library in English. Spanish generally uses the article more often than English in these contexts:

• Voy a la escuela. = I’m going to school.
• Voy al trabajo. = I’m going to work.
• Voy a la biblioteca. = I’m going to the library.

Leaving out the article (✗ a biblioteca) is incorrect in standard Spanish.

In Spain, volver is more common in everyday speech:

• Quiero volver a la biblioteca.
• Volví tarde a casa.

Regresar is also correct and understood, but it sounds a bit more formal or more common in some Latin American varieties.

In most situations you can swap them without changing the meaning:

• Quiero volver a la biblioteca mañana.
• Quiero regresar a la biblioteca mañana.

Both mean I want to go back to the library tomorrow. In Spain, you’ll simply hear volver more often in casual conversation.

You cannot normally put two fully conjugated verbs one after another in this way in Spanish.

• Quiero volver a la biblioteca.
  
  • Quiero (conjugated) + volver (infinitive)

If you say ✗ Quiero voy a la biblioteca, both quiero and voy are conjugated, which is incorrect in this structure.

To express I want to go to the library, Spanish either uses:

• Quiero ir a la biblioteca. (want to go)
  or, as in your sentence:
• Quiero volver a la biblioteca. (want to go back / return)

Yes. Mañana is quite flexible in word order. All of these are correct and natural:

• Quiero volver a la biblioteca mañana.
• Mañana quiero volver a la biblioteca.
• Quiero mañana volver a la biblioteca. (possible, but less usual; sounds slightly more marked/stylized)

The most common in speech are the first two:

• Put mañana at the end, or
• Put mañana at the beginning for emphasis on tomorrow.

They are different:

• mañana (without article) = tomorrow

  • Quiero volver a la biblioteca mañana. = I want to return to the library tomorrow.

• la mañana (with article la) = the morning

  • Quiero volver a la biblioteca por la mañana. = I want to return to the library in the morning.

So:

• mañana = a future day
• la mañana = the first part of the day (morning)

Yes, and the nuance is similar to English:

• Quiero volver a la biblioteca mañana.

  • Direct, clear: I want to go back to the library tomorrow.

• Me gustaría volver a la biblioteca mañana.

  • Softer, more polite or tentative: I would like to go back to the library tomorrow.

Both are grammatically correct; choose quiero for a stronger statement of desire and me gustaría when you want to sound more polite or less demanding.

When volver means to return / go back to a place, and you mention the destination, you normally use a:

• volver a casa
• volver al trabajo
• volver a la biblioteca

You can use volver without a when you are not specifying a destination, or in other meanings:

• Quiero volver. = I want to return / go back. (destination is understood from context)
• Volver a empezar. = to start again (here volver a + infinitive means to do something again)

In your sentence, because you give a specific place (la biblioteca), you need a: volver a la biblioteca.

No. This is an important false friend:

• la biblioteca = the library (you borrow books, study there)
• la librería = the bookshop / bookstore (you buy books)

So:

• Quiero volver a la biblioteca mañana. = I want to go back to the library tomorrow.
• Quiero volver a la librería mañana. = I want to go back to the bookshop tomorrow.