No quiero mirar el móvil todo el rato en la biblioteca.

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Breakdown of No quiero mirar el móvil todo el rato en la biblioteca.

• querer: to want
• en: in
• la biblioteca: the library

Questions & Answers about No quiero mirar el móvil todo el rato en la biblioteca.

Why doesn’t the sentence start with yo (like Yo no quiero…)?

Spanish usually leaves out subject pronouns when the verb ending already shows who the subject is.
In quiero, the -o ending clearly indicates yo (I).
So No quiero mirar el móvil… already means I don’t want to look at the phone…, and yo would only be added for emphasis or contrast (e.g. Yo no quiero, pero él sí = I don’t want to, but he does).

Why is it no quiero mirar instead of something like no miro?

No quiero mirar means I don’t want to look, expressing a desire/intention, not an action happening now.
If you said no miro el móvil todo el rato en la biblioteca, it would mean I don’t look at my phone all the time in the library (a habitual fact about you).
The structure querer + infinitive (quiero mirar) is the normal way to say I want to do X or I don’t want to do X in Spanish.

What’s the difference between mirar and ver here?

Mirar = to look (at), an intentional action.
Ver = to see, more passive; you can see things without trying.

• No quiero mirar el móvil = I don’t want to look at the phone (on purpose).
• No quiero ver el móvil would sound more like I don’t want to see it (have it in my sight), and is less natural in this context.

For “checking your phone”, mirar el móvil is what people typically say.