Ők a könyvtárban tanulnak.

Yes. In Hungarian, the verb ending often already tells you the subject, so tanulnak by itself can mean they study or they are studying.

That means ők is often optional. It is usually included for:

• emphasis: They are studying
• contrast: They are studying, not someone else
• clarity in context

So:

• Tanulnak a könyvtárban. = They are studying in the library.
• Ők a könyvtárban tanulnak. = They are the ones studying in the library / They study in the library.

Ők is the third person plural personal pronoun: they.

Related forms:

• ő = he / she
• ők = they

Hungarian does not usually distinguish he and she in the pronoun ő.

A is the definite article, meaning the.

So:

• a könyvtár = the library
• a könyvtárban = in the library

Hungarian has two forms of the:

• a
• az

Which one is used depends mainly on the sound at the beginning of the next word:

• a before most consonant sounds
• az before vowel sounds

Since könyvtár begins with a consonant, it takes a.

The ending -ban means in.

So:

• könyvtár = library
• könyvtárban = in the library

This is called the inessive case, used for being inside something.

Some examples:

• házban = in the house
• iskolában = in the school
• szobában = in the room

This is because of vowel harmony, a very important feature of Hungarian.

The suffix has two versions:

• -ban
• -ben

Words usually take the version that matches the vowels in the stem.

Könyvtár contains the back vowel á, so it takes the back-vowel form:

• könyvtárban

A word with front vowels would take -ben, for example:

• székben = in the chair
• kertben = in the garden

Tanulnak is the verb tanul = to study / to learn in:

• present tense
• third person plural
• indefinite conjugation

So it means:

• they study
• they are studying

Hungarian present tense can often translate into either simple present or present continuous in English, depending on context.

Hungarian verbs have two main conjugation patterns:

• indefinite
• definite

The choice depends mainly on whether the verb has a definite direct object.

Here, there is no direct object at all:

• Ők a könyvtárban tanulnak. = They are studying in the library.

So Hungarian uses the indefinite form tanulnak.

Compare:

• Tanulnak. = They are studying.
• Tanulják a leckét. = They are studying the lesson.

In the second sentence, a leckét is a definite object, so the verb changes to tanulják.

Yes, those are also possible. Hungarian word order is more flexible than English, and changing the order often changes the focus or emphasis rather than the basic meaning.

For example:

• Ők a könyvtárban tanulnak.
  Emphasizes ők or presents the whole statement with that pronoun included.
• A könyvtárban tanulnak.
  Emphasizes the place: It is in the library that they study.
• Tanulnak a könyvtárban.
  A neutral way to say They are studying in the library.

So the sentence is grammatical, but word order in Hungarian often reflects what is new, important, or contrasted.

It can mean either one.

Hungarian present tense often covers both:

• They study in the library
• They are studying in the library

The exact English translation depends on context.

If the sentence is just describing a general fact, English may use study. If it describes what is happening now, English may use are studying.

A few useful pronunciation points:

• ő is a long vowel, somewhat like a longer version of the vowel in German schön or French peu.
• ö is similar, but shorter.
• á is a long vowel, roughly like a in father.
• ny is pronounced like ny in Spanish señor or like ni in onion.
• Hungarian stress is usually on the first syllable of the word.

So:

• ők has a long ő
• könyvtárban is stressed on the first syllable: KÖNYV-tár-ban

Yes, very often that is actually the more natural form.

You can simply say:

• A könyvtárban tanulnak.
• Tanulnak a könyvtárban.

Because tanulnak already shows they, the pronoun is not required unless you want emphasis, contrast, or clarity.

Exactly. Hungarian often expresses meanings like in, on, to, from, and so on with suffixes attached directly to the noun.

So instead of a separate word like English in, Hungarian often adds an ending:

• könyvtárban = library + in
• házban = house + in
• iskolában = school + in

This is one of the big structural differences between Hungarian and English.

Yes, depending on context, English may translate it as either in the library or sometimes at the library.

The Hungarian form -ban/-ben literally means in, but natural English translation may vary. If the idea is simply location at the library building, English sometimes prefers at the library, even though Hungarian uses the inside location form.