Þegar tíminn er stuttur, set ég svefninn í forgang.

Here Þegar means when and introduces a subordinate clause: Þegar tíminn er stuttur = When time is short.

A common beginner point:

• þegar = when as a conjunction
• hvenær = when in a direct question

So:

• Hvenær kemurðu? = When are you coming?
• Þegar þú kemur, förum við. = When you come, we’ll go.

Also, þegar can mean already in other contexts, but that is not what it means in this sentence.

Because Icelandic usually follows a verb-second pattern in main clauses.

When the sentence begins with the subordinate clause Þegar tíminn er stuttur, that whole clause takes the first slot. The finite verb of the main clause then comes next:

• Þegar tíminn er stuttur, set ég svefninn í forgang.

If you put the main clause first, you get the more familiar order:

• Ég set svefninn í forgang þegar tíminn er stuttur.

So the inversion in set ég is normal and expected.

Set is the 1st person singular present tense of the verb setja = to put / set.

So:

• ég set = I put / I set
• þú setur = you put
• hann/hún/það setur = he/she/it puts

In this sentence, set means I put or more naturally I prioritize because of the full expression setja ... í forgang.

Tíminn is the definite form: the time.

• tími = time
• tíminn = the time

In this sentence, tíminn refers to the time available in the situation being talked about, so the time is natural in Icelandic. English often uses just time in this kind of sentence, but Icelandic may use the definite form where English does not.

Grammatically, tíminn is also the subject of er stuttur.

Because Icelandic adjectives must agree with the noun they describe in gender, number, and case.

Here the noun is tíminn, which is:

• masculine
• singular
• nominative

So the adjective must also be masculine singular nominative:

• stuttur = short

That is why you get:

• tíminn er stuttur

If the noun were different, the adjective form would change too.

Svefninn is the direct object of set, so it is in the accusative.

• svefn = sleep
• svefninn = the sleep

In this particular noun, the definite nominative singular and definite accusative singular look the same in spelling, so you identify the case by its role in the sentence:

• set ég svefninn í forgang
  → I prioritize sleep
  → svefninn is the thing being prioritized, so it is the object.

This is one of those places where Icelandic and English do not match word-for-word.

English often uses a bare noun:

• I prioritize sleep

Icelandic often uses the definite form for something understood as a specific area or item under discussion:

• svefninn = literally the sleep

So here it does not mean one particular instance of sleep. It means sleep as the thing I choose to give priority to.

This is very natural in Icelandic, especially in phrases about priorities such as:

• setja heilsuna í forgang = prioritize health
• setja fjölskylduna í forgang = prioritize family

The dictionary form is forgangur = priority.

After the preposition í here, it appears as forgang because this expression uses the accusative:

• í forgang

That fits a very common Icelandic pattern:

• accusative after a preposition often suggests movement into something or a change of state

So setja svefninn í forgang is literally something like put sleep into priority.

A useful comparison:

• setja X í forgang = put X into priority / prioritize X
  → accusative
• vera í forgangi = be in priority / take priority
  → dative

Yes. Setja eitthvað í forgang is a very common Icelandic expression meaning:

• to prioritize something
• to give something priority

So although the literal meaning is put something into priority, you should learn it as a set expression.

Another possible Icelandic verb is forgangsraða, but setja ... í forgang is very natural and common in everyday use.

Yes, absolutely.

Both versions are natural:

• Þegar tíminn er stuttur, set ég svefninn í forgang.
• Ég set svefninn í forgang þegar tíminn er stuttur.

The difference is mostly about focus and word order:

• starting with Þegar tíminn er stuttur emphasizes the condition first
• starting with Ég set svefninn í forgang starts with the main statement

The important grammar difference is that when the þegar-clause comes first, you get inversion:

• set ég

When it comes later, you keep normal word order:

• ég set

Because the sentence begins with a subordinate clause:

• Þegar tíminn er stuttur

In Icelandic, it is standard to separate an introductory subordinate clause from the main clause with a comma:

• Þegar tíminn er stuttur, set ég svefninn í forgang.

So the comma is normal punctuation here, not optional decoration.