Hún keypti sjampó og klósettpappír, en gleymdi tannþræðinum aftur.

Because gleyma takes the dative case in Icelandic.

• Infinitive: að gleyma einhverju = to forget something
• Base noun: tannþráður = dental floss
• Dative singular: tannþræði
• Dative singular definite: tannþræðinum = the dental floss

So gleymdi tannþræðinum literally means forgot the dental floss, with the noun in the case required by the verb.

The change from þráður to þræði- is just part of the noun’s normal declension pattern.

Because Icelandic often leaves out the subject in the second clause when it is the same as the subject in the first clause.

So:

• Hún keypti sjampó og klósettpappír, en gleymdi tannþræðinum aftur.

means the same as:

• Hún keypti sjampó og klósettpappír, en hún gleymdi tannþræðinum aftur.

The second hún is understood automatically from the first clause.

They are both in the past tense.

• keypti = past tense of að kaupa = to buy
• gleymdi = past tense of að gleyma = to forget

So the sentence is describing completed actions in the past: she bought some things, but forgot one thing.

Because Icelandic does not have an indefinite article like English a/an.

So:

• sjampó can mean shampoo or a shampoo
• klósettpappír can mean toilet paper or some toilet paper

Whether the noun is indefinite or definite is understood from context, or shown with the definite article ending when needed.

That is why you see:

• sjampó
• klósettpappír

but later:

• tannþræðinum = the dental floss

Here aftur means again.

So gleymdi tannþræðinum aftur means forgot the dental floss again.

In other contexts, aftur can also mean back, depending on the sentence. But in this sentence, again is the natural meaning.

En means but, and it introduces a contrast.

• Hún keypti sjampó og klósettpappír = she bought shampoo and toilet paper
• en gleymdi tannþræðinum aftur = but forgot the dental floss again

So en shows that the second part goes against what you might expect: she remembered some items, but not all of them.

Because en is joining two clauses here.

The sentence has:

1. Hún keypti sjampó og klósettpappír
2. (hún) gleymdi tannþræðinum aftur

In Icelandic, it is normal to use a comma before en when it connects two full clauses like this.

Yes. Icelandic uses compound words very often.

• klósett
  • pappír → klósettpappír = toilet paper
• tönn/tanna
  • þráður → tannþráður = dental floss

This is very common in Icelandic, and learning to recognize the parts of compounds is extremely helpful for vocabulary building.

Sjampó is a loanword, and in everyday Icelandic it is commonly treated as a noun that often stays the same in form, especially for beginners’ purposes.

So in a sentence like this, you can simply read:

• sjampó = shampoo

without worrying much about declension right away.

The more important grammar point in this sentence is actually the clearly declined noun tannþræðinum, because that shows the dative required by gleyma.

Then the nouns would usually take the definite article as a suffix, just like tannþræðinum does.

A more definite version could look like:

• Hún keypti sjampóið og klósettpappírinn, en gleymdi tannþræðinum aftur.

That would mean:

• She bought the shampoo and the toilet paper, but forgot the dental floss again.

So Icelandic usually marks definiteness by adding it to the end of the noun, rather than using a separate word like English the.