Últimamente estudio mucho en la biblioteca.

Because Spanish usually drops subject pronouns when the verb already makes the subject clear.

• estudio = I study
• The -o ending tells you it is yo

So:

• Últimamente estudio mucho en la biblioteca.
• Últimamente yo estudio mucho en la biblioteca.

Both are grammatical, but the version without yo is more natural unless you want emphasis or contrast:

• Yo estudio mucho, pero mi hermano no.
  = I study a lot, but my brother doesn’t.

Spanish often uses the simple present for actions that are habitual, repeated, or true around the present time.

Here, estudio means something like:

• I study
• I’ve been studying
• I study a lot lately / these days

Because últimamente already gives the idea of lately, the present tense sounds very natural.

If you wanted to sound more explicitly progressive, you could say:

• Últimamente estoy estudiando mucho en la biblioteca.

That also works, but estudio is simpler and very common.

Últimamente means lately or recently, especially referring to the recent period of time up to now.

So it sets the time frame for the whole sentence.

Examples:

• Últimamente duermo poco. = Lately I sleep little.
• Últimamente hace mucho calor. = Lately it’s been very hot.

It is not the same as finalmente.
Even though últimamente comes from último, it does not mean finally.

No. Spanish word order is flexible, especially with adverbs like últimamente.

These are all possible:

• Últimamente estudio mucho en la biblioteca.
• Estudio mucho en la biblioteca últimamente.
• Estudio últimamente mucho en la biblioteca. (less natural)

The most natural placement here is at the beginning, because it clearly sets the context right away.

Here mucho means a lot.

In Spanish, when mucho modifies a verb, it usually comes after the verb:

• estudio mucho = I study a lot
• trabaja mucho = he/she works a lot

This is different from English, where a lot often comes later in the sentence.

Also, here mucho is an adverb, so it does not change form:

• Yo estudio mucho
• Ella estudia mucho

But when mucho is an adjective, it does change:

• mucho trabajo
• muchos libros
• mucha comida

Because en means in / at, while a usually indicates movement toward a place.

• Estudio en la biblioteca = I study in / at the library
• Voy a la biblioteca = I go to the library

So:

• en la biblioteca = location
• a la biblioteca = destination

Spanish uses articles more often than English.

So when talking about a place like the library, Spanish normally says:

• en la biblioteca

Omitting the article here would usually sound incomplete or unnatural in standard usage.

This is very common with places:

• Estoy en la escuela
• Trabajo en la oficina
• Ceno en el restaurante

Yes: biblioteca means library.

This is a very common confusion for English speakers because it looks a bit like bibliotheca or something book-related in English.

Important distinction:

• biblioteca = library
• librería = bookshop / bookstore

So:

• Estudio en la biblioteca = I study in the library
• Compro libros en la librería = I buy books in the bookshop

Yes, you could say:

• Últimamente estoy estudiando mucho en la biblioteca.

That means something like Lately I’ve been studying a lot in the library.

The difference is subtle:

• estudio = more general, habitual, simple statement
• estoy estudiando = emphasizes the ongoing process more

In this sentence, both are correct, but estudio is very natural and concise.

It tells you where the studying happens.

So the sentence breaks down like this:

• Últimamente = lately
• estudio = I study
• mucho = a lot
• en la biblioteca = in/at the library

It is a prepositional phrase of place, introduced by en.

Because Spanish accent marks show which syllable is stressed when the word does not follow the default stress rules.

Últimamente is pronounced with stress on ÚL:

• ÚL-ti-ma-men-te

Without the accent, the stress would be interpreted differently.

A useful tip: many adverbs ending in -mente keep the written accent of the original adjective if it had one.

For example:

• última → últimamente
• rápida → rápidamente

A simple pronunciation guide is:

OOL-tee-ma-men-teh es-TOO-dyo MOO-cho en la byblyo-TEH-ka

A few points:

• ú in Últimamente is stressed
• estudio is usually pronounced roughly es-TOO-dyo
• biblioteca is stressed on te: bi-blio-TE-ca
• In Spain, c before e in biblioteca is pronounced like the th in thin in much of Spain: biblio-te-tha
• In Latin America and some parts of Spain, it sounds like s: biblio-te-sa

So in standard Peninsular Spanish, you may hear:

OOL-tee-ma-men-te es-TOO-dyo MOO-cho en la byblyo-TEH-tha