Eftir að hafa borgað hundagjaldið notar umráðamaðurinn lausagöngusvæðið og athugar ábyrgðartrygginguna.

Eftir að hafa borgað literally means after having paid.

This is a very common Icelandic pattern:

• eftir = after
• að hafa = to have
• borgað = paid

So eftir að hafa + past participle/supine expresses after doing something or after having done something.

In natural English, you might translate it more simply as:

• After paying the dog fee...
• After having paid the dog fee...

The subject is not repeated in this phrase. It is understood to be the same person as the subject of the main clause, here umráðamaðurinn.

After hafa in this construction, Icelandic uses the supine form, which often looks like the neuter singular participle form. For borga, that form is borgað.

So:

• hafa borgað = have paid
• að hafa borgað = to have paid

You do not use an agreeing adjective-like participle here. In other words, borgað is part of the verbal construction, not a descriptive adjective agreeing with a noun.

This is similar to English have paid, where paid stays the same.

This is because Icelandic normally follows a verb-second pattern in main clauses.

The first slot in the sentence is taken by the introductory phrase:

• Eftir að hafa borgað hundagjaldið

Once that comes first, the finite verb usually comes next:

• notar

Then the subject follows:

• umráðamaðurinn

So the structure is:

• [Introductory phrase] + [finite verb] + [subject] + ...

If there were no introductory phrase, you would normally get:

• Umráðamaðurinn notar lausagöngusvæðið...

This verb-second word order is one of the most important things for English speakers to notice in Icelandic.

Umráðamaðurinn means something like:

• the person in charge
• the keeper
• the custodian
• in context, often the owner or the person responsible for the dog

It comes from:

• umráðamaður = person with control/responsibility
• -inn = the suffixed definite article, so the

So:

• umráðamaður = a person responsible
• umráðamaðurinn = the person responsible

In rules, regulations, and official language, Icelandic often prefers words like this over simpler everyday wording.

Icelandic usually expresses the with a suffix attached to the noun, rather than with a separate word like English the.

Examples from this sentence:

• umráðamaðurinn = the person responsible
• hundagjaldið = the dog fee
• lausagöngusvæðið = the off-leash area
• ábyrgðartrygginguna = the liability insurance (in accusative)

So instead of writing a separate word for the, Icelandic often adds an ending such as:

• -inn
• -ið
• -una

The exact form depends on the noun’s gender, number, and case.

Hundagjaldið is the direct object of borgað, so it is in the accusative.

The noun is:

• hundagjald = dog fee
• neuter singular

For many neuter nouns in Icelandic, the nominative and accusative singular look the same, so the form hundagjaldið could look unchanged on the surface. But its function here is accusative because borga takes a direct object.

Breakdown:

• hundagjald = dog fee
• hundagjaldið = the dog fee

Both are direct objects, so they are also in the accusative.

1. lausagöngusvæðið

   • object of notar = uses
   • noun: lausagöngusvæði = off-leash area
   • neuter singular definite
   • nominative and accusative are the same in this form

2. ábyrgðartrygginguna

   • object of athugar = checks
   • noun: ábyrgðartrygging = liability insurance
   • feminine singular definite accusative

That is why this one has the clearly accusative-looking ending -una.

So the verbs govern these objects like this:

• nota
  • accusative
• athuga
  • accusative

Yes. Icelandic uses compounds constantly, and breaking them up is very helpful.

Here are the main ones:

• hundagjald

  • hunda- = dog/dogs
  • gjald = fee
  • so: dog fee

• lausagöngusvæði

  • lausaganga = free roaming / being off leash
  • svæði = area
  • so: off-leash area or free-roaming area

• ábyrgðartrygging

  • ábyrgð = responsibility / liability
  • trygging = insurance
  • so: liability insurance

Learning to spot the parts of compounds is one of the fastest ways to improve your Icelandic vocabulary.

They are both present tense, third person singular forms.

• nota = to use

• notar = uses

• athuga = to check
• athugar = checks

The subject is singular:

• umráðamaðurinn = the person responsible

So the verbs are singular too.

This corresponds to English:

• the person uses
• the person checks

Yes. The understood subject of að hafa borgað hundagjaldið is the same as umráðamaðurinn.

So the sentence means that the person responsible is the one who:

• paid the dog fee,
• uses the off-leash area,
• and checks the liability insurance.

Icelandic often leaves that repeated subject unstated in non-finite phrases like this, just as English can do in sentences like:

• After paying the fee, the owner enters.

Because the two verbs are joined by og = and, and they share the same subject:

• notar = uses
• athugar = checks

So:

• umráðamaðurinn notar lausagöngusvæðið og athugar ábyrgðartrygginguna

means:

• the person responsible uses the off-leash area and checks the liability insurance

This is exactly like English, where one subject can govern multiple verbs:

• The owner pays, enters, and checks the documents.

Yes, if you change the sentence structure.

For example:

• Umráðamaðurinn notar lausagöngusvæðið eftir að hafa borgað hundagjaldið og athugar ábyrgðartrygginguna.

But in the original sentence, the writer wants to foreground the after paying... condition first. Once that phrase is placed first, Icelandic normally puts the finite verb in second position:

• Eftir að hafa borgað hundagjaldið notar umráðamaðurinn...

So the original word order is very natural and very Icelandic.