Learn Hardcore German: Ich gehe zur Bibliothek, um Deutsch zu lernen. - I am going to the library in order to study German.

In spoken and written German, this contraction is very common and sounds more natural here. Both zu der Bibliothek and zur Bibliothek are grammatically correct, but zur is what people normally say.

Why is it zu(r) Bibliothek and not in die Bibliothek or nach der Bibliothek?

Different prepositions have different typical uses:

zu is used for going to people or places as destinations, especially institutions:
- zur Bibliothek (to the library)
- zur Schule (to school)
- zum Arzt (to the doctor)
in
- accusative (in die Bibliothek) emphasizes going into the building/inside a space.
- Ich gehe in die Bibliothek. = I’m going into the library.
nach is used mainly with cities, countries, and “home” (nach Hause):
- nach Berlin, nach Deutschland, nach Hause.

So zur Bibliothek is the standard, idiomatic way to say “to the library” as a destination. In die Bibliothek is also possible but slightly shifts the focus to entering the building.

Why is Bibliothek in the dative case here?

The preposition zu always takes the dative case.

Nominative: die Bibliothek
Dative singular feminine: der Bibliothek

So we need zu der Bibliothek → contracted to zur Bibliothek.
That’s why Bibliothek is in the dative: the preposition zu forces the dative.

Why does um Deutsch zu lernen have a comma before it?

In German, an infinitive clause with um … zu (or also with ohne … zu, anstatt … zu) is normally separated from the main clause by a comma.

Main clause: Ich gehe zur Bibliothek
Infinitive purpose clause: um Deutsch zu lernen

The comma marks the boundary between the main action and the purpose clause:
Ich gehe zur Bibliothek, um Deutsch zu lernen.

What does the structure um Deutsch zu lernen mean exactly?

um … zu + infinitive expresses purpose: “in order to do something.”

Structure:

um
- [object / extra info]
  - zu
    - [infinitive verb]

Here:

um (in order)
Deutsch (what you are going to learn)
zu lernen (to learn)

So um Deutsch zu lernen = “in order to learn German” / “to learn German (as the purpose).”

This structure is very common when you want to express why you do something:

Ich lerne Deutsch, um in Deutschland zu arbeiten.
(I’m learning German (in order) to work in Germany.)

Why is it Deutsch lernen and not lernen Deutsch?

In German infinitive phrases, the object normally comes before the infinitive verb:

Deutsch lernen = literally “German learn”

You almost never say lernen Deutsch in standard German when the verb is at the end. So:

um Deutsch zu lernen (correct)
um lernen Deutsch (wrong)

This is the same pattern as:

etwas essen (to eat something)
ein Buch lesen (to read a book)

Why is Deutsch capitalized here?

Deutsch is capitalized because it is used as a noun (the German language), not as an adjective.

As a language noun:
- Ich lerne Deutsch. (I’m learning German.) → capitalized.
As an adjective:
- die deutsche Sprache (the German language) → deutsche is an adjective, lowercase.

In your sentence, Deutsch = “the German language,” so it is written with a capital D.

What is the difference between Deutsch lernen and Deutsch studieren?

Both can be translated as “to study/learn German,” but they are used differently:

Deutsch lernen
- Very general: learning the language at any level, in any context.
- Can be self-study, a course, app, etc.
- Most common expression.
Deutsch studieren
- Usually means studying German as an academic subject at university (German language/literature/linguistics).
- Implies a formal degree program.

So in your sentence, um Deutsch zu lernen is correct and natural. um Deutsch zu studieren would suggest you’re going there to pursue academic German studies (e.g., as your major).

Why is the verb gehe in the second position?

German main clauses follow the V2 rule (verb-second rule):
The finite verb (the conjugated verb) must be in the second position in the sentence.

Ich (1st element)
gehe (2nd element = finite verb)
zur Bibliothek (rest of the clause)
, um Deutsch zu lernen. (extra clause)

If you move some other element to the front, the verb is still second:

Heute gehe ich zur Bibliothek, um Deutsch zu lernen.
(Heute = 1st element, gehe = 2nd element)

Can I say Ich fahre zur Bibliothek instead of Ich gehe zur Bibliothek?

Yes, but it slightly changes the picture:

gehen = to go on foot (walk)
fahren = to go by vehicle (car, bike, bus, train, etc.)

So:

Ich gehe zur Bibliothek. → I’m walking to the library.
Ich fahre zur Bibliothek. → I’m going to the library by some kind of transport.

Both are correct; you choose depending on how you travel.

Why is the verb lernen at the very end of the sentence?

In German subordinate/infinitive clauses, the verb (or infinitive) goes to the end.

The clause um Deutsch zu lernen is an infinitive clause of purpose. In such clauses, the infinitive appears at the end of the clause, and zu is placed directly before the infinitive:

um Deutsch zu lernen
(not: um zu Deutsch lernen and not: um Deutsch lernen zu)

So the order is: um + object(s) + zu + infinitive (at the end).

Could I express the same meaning with damit instead of um … zu?

Yes, but the structure changes, and it sounds slightly more formal:

Ich gehe zur Bibliothek, damit ich Deutsch lerne.

Key differences:

um … zu + infinitive
- Same subject in both parts of the sentence (I go / I learn).
- More compact: Ich gehe zur Bibliothek, um Deutsch zu lernen.
damit + full clause
- Often used when the subject of the purpose clause can be different:
  - Ich spreche langsam, damit du alles verstehst.
- You must conjugate the verb: damit ich Deutsch lerne, not infinitive.

For your sentence, um Deutsch zu lernen is the most natural and common choice.