Biblioteket ligger tæt på universitetet.

In Danish, -et is often the definite ending for neuter nouns. It means the.

So:

• et bibliotek = a library
• biblioteket = the library

And:

• et universitet = a university
• universitetet = the university

Unlike English, Danish usually adds the to the end of the noun instead of putting a separate word in front of it.

Because Danish normally uses a suffixed definite article.

English says:

• the library
• the university

Danish usually says:

• biblioteket
• universitetet

So the idea of the is already built into the noun. That is why you do not need a separate word before it here.

Ligger literally means lies or is situated. In this sentence, it is used to talk about location.

So:

• Biblioteket ligger tæt på universitetet = The library is located close to the university

Danish often uses ligge for the position of places and buildings.

Compare:

• Biblioteket ligger i centrum = The library is in the city center
• Huset ligger ved søen = The house is by the lake

You can sometimes use er in Danish for location, but ligger is very common and often sounds more natural when talking about where a place is situated.

Tæt på means close to or near.

It is a fixed expression:

• tæt = close/tight
• på = on/to, but here it works as part of the expression tæt på

So you should learn tæt på as a unit meaning close to.

Examples:

• Skolen ligger tæt på stationen = The school is close to the station
• Jeg bor tæt på arbejde = I live close to work

No, but it is one of the most common and useful ways.

Other possibilities include:

• nær = near
  This exists, but in everyday Danish it is often less common than tæt på in many contexts.
• i nærheden af = in the vicinity of / near
  This is a bit longer and more formal or descriptive.

For a learner, tæt på is a very good, natural choice.

This is the normal Danish word order for a simple statement:

• Subject
  • verb
    • rest of sentence

So here:

• Biblioteket = subject
• ligger = verb
• tæt på universitetet = expression of place/location

That is very similar to English:

• The library
  • is located
    • close to the university

Danish main clauses usually keep the verb in the second position, and this sentence follows that pattern perfectly.

The dictionary form is ligge.

So:

• at ligge = to lie / to be situated
• ligger = lies / is situated

This -r form is the usual present tense in Danish.

Examples:

• Hotellet ligger ved stranden = The hotel is by the beach
• Bogen ligger på bordet = The book is lying on the table

You would use the indefinite forms:

• Et bibliotek ligger tæt på et universitet

Grammatically, that means:

• A library is close to a university

But in real usage, this sounds more general and less specific. The original sentence refers to specific places:

• Biblioteket ligger tæt på universitetet = The library is close to the university

A rough learner-friendly guide:

• biblioteket ≈ bee-blee-oh-TEK-ed
• universitetet ≈ oo-nee-ver-see-TEH-ded

A few important notes:

• The final -et is often pronounced quite lightly.
• Danish pronunciation is usually softer and less clearly pronounced than spelling suggests.
• The d/t sounds at the end may sound weaker than an English speaker expects.

If you are learning pronunciation, it is best to listen to native audio, because Danish spelling and pronunciation often do not match in a fully predictable way.

Danish nouns have grammatical gender, and the two common genders for learners are often taught as:

• en-words
• et-words

Both of these nouns are et-words:

• et bibliotek
• et universitet

That is why their definite forms become:

• biblioteket
• universitetet

Unfortunately, noun gender in Danish often has to be memorized, although some word endings can give clues. Words ending in -tek or -tet do not automatically follow one rule, so it is safest to learn each noun with its article: et bibliotek, et universitet.

Not naturally. A word-for-word translation can help you see the structure, but it is not how English says it.

Literally, you might break it down as:

• ligger = lies
• tæt på = close to

But natural English would be:

• is close to
• is near
• is located close to

So it is better to understand the phrase by meaning rather than translate every word literally.