Auk þess að skoða málverkið skoðar kaupandinn leirmuninn og verðmiðann.

Auk þess að means in addition to, besides, or as well as.

So:

• Auk þess að skoða málverkið = In addition to looking at the painting
• Then the main clause says what else the buyer is looking at.

A very literal breakdown is:

• auk = increase/addition
• þess = of that
• að = to

But it is best learned as one fixed expression: auk þess að + infinitive.

Because the sentence contains two different parts:

1. auk þess að skoða málverkið
   Here skoða is an infinitive, meaning to look at / to examine.

2. skoðar kaupandinn leirmuninn og verðmiðann
   Here skoðar is a finite verb, meaning looks at / examines.

So the sentence is basically:

• Besides looking at the painting,
• the buyer looks at the ceramic object and the price tag.

English sometimes avoids repeating the same verb, but Icelandic often keeps the structure clear by doing so.

Because they are different verb forms.

• skoða = infinitive = to look at
• skoðar = present tense = looks at / is looking at

After að in auk þess að, you use the infinitive:

• að skoða = to look at

In the main clause, you need a conjugated verb that agrees with the subject:

• kaupandinn skoðar = the buyer looks at

This is because of Icelandic V2 word order in main clauses.

When something other than the subject comes first, the finite verb usually has to come second. Here, the sentence starts with the adverbial phrase:

• Auk þess að skoða málverkið

So in the main clause, the finite verb comes next:

• skoðar

And only after that comes the subject:

• kaupandinn

So the order is:

• fronted phrase
• finite verb
• subject

That is why you get:

• Auk þess að skoða málverkið skoðar kaupandinn ...

rather than:

• Auk þess að skoða málverkið kaupandinn skoðar ...

They are all in the accusative case because they are direct objects of skoða.

The verb skoða takes an accusative object, so:

• skoða málverkið = look at the painting
• skoða leirmuninn = look at the ceramic object
• skoða verðmiðann = look at the price tag

So the case pattern is:

• subject in nominative: kaupandinn
• objects in accusative: málverkið, leirmuninn, verðmiðann

Those endings include the definite article, which in Icelandic is usually attached to the end of the noun.

So instead of a separate word like the, Icelandic often uses a suffix.

Examples from the sentence:

• málverk = painting

• málverkið = the painting

• leirmunur = ceramic object / artifact

• leirmuninn = the ceramic object

• verðmiði = price tag
• verðmiðann = the price tag

The exact form of the ending depends on:

• the noun’s gender
• its declension class
• the case
• the number

So these endings are not random; they reflect Icelandic noun grammar.

The base form is kaupandi, which means buyer.

In this sentence, it appears as kaupandinn, which means the buyer.

So:

• kaupandi = buyer
• kaupandinn = the buyer

Here it is in the nominative singular definite, because it is the subject of the main clause.

In many contexts, skoða means look at, examine, or inspect rather than just see.

In this sentence, look at is a good natural translation, but examine also fits well because the buyer is looking at several objects carefully.

Compare roughly:

• sjá = see
• horfa á = watch / look at something with your eyes directed toward it
• skoða = look at carefully / inspect / examine

So skoða often suggests a more deliberate look.

In English, you might often write:

• In addition to looking at the painting, the buyer looks at...

with a comma.

In Icelandic, punctuation does not always match English punctuation exactly, and a comma is often not used after a fronted phrase like this. So:

• Auk þess að skoða málverkið skoðar kaupandinn ...

is normal.

In other words, the lack of a comma is not strange in Icelandic.

It can do both, but the structure changes.

With a verb, you often get:

• auk þess að skoða málverkið = in addition to looking at the painting

With a noun phrase, you can also have:

• auk málverksins = in addition to the painting

So in your sentence, auk þess að + infinitive is specifically the pattern for in addition to doing something.

A useful breakdown is:

• Auk þess að = besides / in addition to
• skoða = to look at / examine
• málverkið = the painting
• skoðar = looks at / examines
• kaupandinn = the buyer
• leirmuninn = the ceramic object
• og = and
• verðmiðann = the price tag

So a very literal version would be:

• Besides to look at the painting, looks the buyer at the ceramic object and the price tag.

That is not good English, but it helps show the Icelandic structure.

A natural English translation would be:

• Besides looking at the painting, the buyer also looks at the ceramic object and the price tag.

Yes. A more straightforward subject-first version would be:

• Kaupandinn skoðar leirmuninn og verðmiðann auk þess að skoða málverkið.

That still means essentially the same thing: the buyer looks at the ceramic object and the price tag, in addition to looking at the painting.

The original sentence puts auk þess að skoða málverkið first for emphasis or flow. When that phrase is fronted, the main clause follows V2 word order, which is why skoðar comes before kaupandinn.