Ved indgangen står en automat, hvor vi kan købe billetter.

Because Danish normally follows the verb-second (V2) rule in main clauses.

The sentence begins with Ved indgangen (“at/by the entrance”), and that takes the first position. In a Danish main clause, the finite verb must then come next, so you get:

Ved indgangen står en automat

Literally, the order is something like:

At the entrance stands a machine

If the sentence started with the subject, then it would be:

En automat står ved indgangen.

Both are grammatical, but the original version puts more focus on where the machine is.

Ved here means by, at, or near.

So Ved indgangen means something like:

• by the entrance
• at the entrance
• near the entrance

It does not usually mean being physically inside something. It is more about location next to or at a place.

Because indgangen is the definite form: the entrance.

In Danish, definiteness is often added as an ending:

• en indgang = an entrance
• indgangen = the entrance

So Ved indgangen means at the entrance, probably a specific entrance already understood from the context.

Danish often uses position verbs where English would simply use is or there is.

So:

• står = stands
• ligger = lies / is located
• sidder = sits

For objects that are upright or placed somewhere, Danish often says they stand. A machine is treated as something physically standing there.

So:

Ved indgangen står en automat
literally: At the entrance stands a machine

In natural English, we would usually say:

There is a machine at the entrance.

En automat means a machine, often a self-service machine.

Depending on context, it could be:

• a ticket machine
• a vending machine
• some other kind of automatic machine

Because the sentence continues with hvor vi kan købe billetter, it clearly means a ticket machine here.

Also note that automat is a common-gender noun, so it takes en:

• en automat
• automaten

Here hvor means where.

It introduces a clause referring back to a place:

en automat, hvor vi kan købe billetter
= a machine where we can buy tickets

This is very natural in Danish when talking about a location or place-like thing.

So hvor connects the machine with the action happening there.

Because Danish uses commas before subordinate clauses much more regularly than English does.

Here, hvor vi kan købe billetter is a subordinate clause, so it is separated by a comma:

Ved indgangen står en automat, hvor vi kan købe billetter.

In English, you might or might not expect a comma in similar wording, but in Danish this comma is standard.

Because after a modal verb like kan (“can”), Danish uses the bare infinitive without at.

So:

• vi kan købe = we can buy
• not vi kan at købe

This works like English:

• we can buy
• not we can to buy

Other common modal verbs in Danish work the same way:

• vil købe = want to buy / will buy
• skal købe = must / have to buy
• må købe = may / be allowed to buy

Billetter is the indefinite plural form: tickets.

Forms:

• en billet = a ticket
• billetten = the ticket
• billetter = tickets
• billetterne = the tickets

In this sentence, the meaning is general: we can buy tickets there. Danish often leaves out a word like some when it is not needed.

So:

vi kan købe billetter
= we can buy tickets

If you said billetterne, it would mean the tickets, referring to specific tickets already known.

Yes. A very natural alternative would be:

Der er en automat ved indgangen, hvor vi kan købe billetter.

That means:

There is a machine at the entrance where we can buy tickets.

The difference is mainly style and focus:

• Ved indgangen står en automat ... puts the location first and sounds a bit more descriptive.
• Der er en automat ved indgangen ... is a straightforward way to introduce that something exists somewhere.

Both are good Danish.

Yes. Købe is the infinitive, meaning to buy.

Some useful forms are:

• at købe = to buy
• køber = buy / buys
• købte = bought
• har købt = have bought

In this sentence, after kan, Danish uses the infinitive without at:

vi kan købe billetter
= we can buy tickets

It breaks down like this:

Ved indgangen = adverbial of place
står = finite verb
en automat = subject
hvor vi kan købe billetter = subordinate clause describing the machine

So the overall idea is:

At the entrance, there is a machine where we can buy tickets.

This is a good example of two important Danish patterns at once:

1. V2 word order in the main clause
2. a subordinate clause introduced by hvor