Jeg må kontakte tandlægevagten.

Here må means must / have to / need to.

In Danish, må can have a few related meanings depending on context:

• obligation/necessity: Jeg må kontakte tandlægevagten = I must contact the emergency dentist service
• permission: Må jeg gå? = May I go?
• sometimes probability in certain contexts

In this sentence, it clearly expresses necessity, not permission.

Because after a modal verb in Danish, the next verb is normally in the infinitive without at.

Common modal verbs include:

• kan = can
• skal = shall / must / have to
• vil = will / want to
• må = must / may
• bør = should

So:

• Jeg må kontakte
• Jeg kan komme
• Jeg skal gå

Not:

• Jeg må at kontakte

The word at is often like English to, but it is not used after modal verbs.

Kontakte is the infinitive form of the verb, meaning to contact.

That happens because it follows the modal verb må. After a modal, the main verb stays in the infinitive:

• Jeg må kontakte
• Du må vente
• Vi må ringe

If you wanted the present tense without a modal, you would say:

• Jeg kontakter tandlægevagten = I am contacting / I contact the emergency dentist service

Tandlægevagten is a compound noun:

• tandlæge = dentist
• vagt = watch, duty, emergency service, on-call service
• -en = the

So tandlægevagten means something like:

• the emergency dentist service
• the on-call dentist
• the dental emergency service

The exact English translation can vary a little depending on the healthcare system, but the idea is an urgent / out-of-hours dental service.

Because Danish usually marks the definite form of a noun with an ending, instead of a separate word like English the.

Here:

• en tandlægevagt = an emergency dentist service / an on-call dentist
• tandlægevagten = the emergency dentist service / the on-call dentist

This is very common in Danish:

• en bil → bilen = the car
• et hus → huset = the house
• en læge → lægen = the doctor

So the -en at the end is the definite article.

Because in Danish, a noun by itself usually takes a suffix for definiteness.

So English:

• the dentist

often corresponds to Danish:

• tandlægen

not a separate article plus noun.

A separate definite word like den/det/de is used in some other situations, especially with adjectives:

• tandlægevagten = the emergency dentist service
• den nye tandlægevagt = the new emergency dentist service

So in your sentence, the ending -en already does the job of the.

Yes. Danish very often joins nouns together into one compound word.

So:

• tandlæge
  • vagt → tandlægevagt
• then the definite ending gives tandlægevagten

This is completely normal in Danish. English sometimes writes similar ideas as two words, hyphenated words, or compounds, but Danish often prefers a single word.

Other examples:

• sygehus = hospital
• lægehus = medical clinic
• sommerferie = summer holiday

A good habit for learners is to look for the smaller parts inside long Danish words.

Yes. This is the normal word order for a simple main clause:

• Jeg = subject
• må = finite verb
• kontakte tandlægevagten = rest of the predicate

So the structure is:

subject + finite verb + infinitive + object

Danish is a V2 language, which means the finite verb normally comes in the second position in main clauses. Since jeg is first, må comes second.

Yes. In a yes/no question, the finite verb usually comes before the subject:

• Må jeg kontakte tandlægevagten? = May / Must I contact the emergency dentist service?

So compared with the statement:

• Jeg må kontakte tandlægevagten.

the question changes to:

• Må jeg kontakte tandlægevagten?

That verb-subject inversion is very common in Danish.

Må is pronounced roughly like English more without a strong r, or like a long aw sound.

Important points:

• å is a vowel sound, not a + o
• it is a long vowel here
• the word is very short, just one syllable

A rough learner-friendly guide is:

• må ≈ maw

But it is best to listen to native audio, because Danish vowel quality can be tricky.

A rough breakdown is:

• tand
• læge
• vagten

But in natural speech, Danish often reduces unstressed syllables, so it may sound smoother and less fully pronounced than the spelling suggests.

A very rough learner guide might be:

• TAN-lay-veh-vak-dn

But that is only approximate.

A few pronunciation notes:

• æ in læge is a front vowel, somewhat like the vowel in cat, but not exactly
• g in Danish can be softer than English learners expect
• final syllables are often reduced in casual speech

If you want to pronounce it well, it helps to learn the parts separately first:

• tandlæge
• vagt
• tandlægevagten

Yes, but it is not exactly the same.

Both må and skal can sometimes be translated as must, but they often feel different:

• må = necessity, often because the situation requires it
• skal = obligation, plan, instruction, or something decided

So:

• Jeg må kontakte tandlægevagten = I need to contact the emergency dentist service
• Jeg skal kontakte tandlægevagten = I am supposed to / I will / I have to contact the emergency dentist service

In many real situations, either could work, but må often sounds more like this is necessary now.

Yes. That is another very common way to express necessity.

• Jeg må kontakte tandlægevagten
• Jeg er nødt til at kontakte tandlægevagten

Both can mean I have to contact the emergency dentist service.

The second version is often felt as a bit more explicit: I am forced / I need / I have no choice but to.

Notice the grammar difference:

• after må, no at
• after er nødt til, you use at before the infinitive

So:

• Jeg må kontakte
• Jeg er nødt til at kontakte

Yes. Kontakte is normally used directly with the person or service being contacted.

So Danish says:

• kontakte tandlægevagten
• kontakte lægen
• kontakte politiet

You do not need a preposition like to or with here.

That is similar to English contact someone.

Yes. Danish jeg is normally written with a lowercase j, unlike English I, which is always capitalized.

So:

• jeg = normal form inside a sentence
• Jeg = capitalized here only because it begins the sentence

For example:

• Hvis jeg må, kontakter jeg tandlægevagten.

Both jeg forms are lowercase unless they start a sentence.