Sólgleraugun eru á borðinu við hliðina á pennanum.

Because sólgleraugu is normally treated as a plural noun in Icelandic, just like glasses or sunglasses in English.

Even though it refers to one physical item, grammatically it behaves as plural:

• sólgleraugu = sunglasses
• sólgleraugun = the sunglasses

So Icelandic uses a plural verb with it.

Because the subject, sólgleraugun, is grammatically plural.

The verb að vera = to be changes like this in the present tense:

• er = is
• eru = are

So:

• Sólgleraugun eru ... = The sunglasses are ...

If the subject were singular, you would use er instead.

Icelandic makes a lot of compound words, and they are usually written as one word.

Here:

• sól = sun
• gleraugu = glasses

So:

• sólgleraugu = sunglasses

Then the definite form is made from the whole compound:

• sólgleraugun = the sunglasses

This is very normal in Icelandic.

Icelandic usually does not use a separate word for the. Instead, the definite article is attached to the end of the noun.

In this sentence:

• sólgleraugun = the sunglasses
• borðinu = the table (in dative form)
• pennanum = the pen (in dative form)

So instead of a separate word like English the, Icelandic adds an ending to the noun.

Because á can take different cases depending on whether you mean location or movement.

Here it means location: the sunglasses are already on the table.
So Icelandic uses the dative:

• á borðinu = on the table

If something were moving onto the table, Icelandic would usually use the accusative:

• að setja það á borðið = to put it onto the table

So:

• á borðinu = on the table, at rest
• á borðið = onto the table, motion toward it

That ending shows that borð is:

• singular
• definite
• dative

The basic noun is:

• borð = table

In this sentence, after á with a location meaning, it becomes:

• borðinu = the table

So the ending is not random; it tells you the grammatical role of the word.

It means next to or beside.

Literally, it is something like by the side of:

• við = by/at
• hliðina = the side
• á = of/from the perspective of the phrase

But it is best to learn við hliðina á as a fixed expression meaning:

• next to
• beside

So in the sentence:

• við hliðina á pennanum = next to the pen

Because við hliðina á is the normal fixed phrase.

Learners often expect something more literal, but in everyday Icelandic, next to is commonly expressed with:

• við hliðina á

So it is best to memorize the whole chunk as one unit.

In other words, don’t over-analyze it as if each word had to match English perfectly. The phrase as a whole means next to.

Because penni changes form after the phrase við hliðina á.

The noun after á in this expression is in the dative, so:

• penni = pen
• pennanum = the pen

So:

• við hliðina á pennanum = next to the pen

If it were indefinite, you would get:

• við hliðina á penna = next to a pen

It is the same spelling, but not the same meaning.

In Icelandic:

• við can be the pronoun we
• við can also be a preposition, as it is here

In this sentence, it is clearly a preposition because it is part of the phrase:

• við hliðina á = next to

So context tells you which við you are dealing with.

Yes. Icelandic word order is more flexible than English, but the finite verb usually stays in the second position in a main clause.

So you could also say:

• Á borðinu við hliðina á pennanum eru sólgleraugun.

That still means the same thing, but the emphasis changes slightly. It puts more focus on the location first.

A natural indefinite version would be:

• Sólgleraugu eru á borði við hliðina á penna.

That means:

• Sunglasses are on a table next to a pen

Notice the differences:

• sólgleraugun → sólgleraugu
• borðinu → borði
• pennanum → penna

So removing the changes the noun endings too.

Here it is in the nominative, because it is the subject of the sentence.

You can tell it is the thing that is somewhere:

• Sólgleraugun eru ... = The sunglasses are ...

So even though several other nouns in the sentence are in the dative because of prepositions, sólgleraugun stays nominative because it is the subject.