Learn Hardcore Icelandic: Ég hef ekki áhyggjur, því að kennarinn hjálpar. - I am not worried, because the teacher helps.

Icelandic expresses “to be worried” with the idiom hafa áhyggjur (“to have worries”), not with the verb vera (“to be”). So you say Ég hef áhyggjur (I’m worried), never Ég er áhyggjur. If you want to use an adjective with vera, you can say:

Ég er áhyggjufullur (male) / Ég er áhyggjufull (female) = I’m worried/anxious.

Why is áhyggjur plural?

Áhyggjur is practically a plural-only noun (pluralia tantum). You almost always see it in the plural to mean “worries/concerns.” That’s why modifiers also go in feminine plural:

miklar áhyggjur (a lot of worries)
engar áhyggjur (no worries)

How do I say what I’m worried about?

Use the preposition af with the dative:

Ég hef áhyggjur af prófinu. (I’m worried about the exam.)
Hún hefur áhyggjur af heilsu hans. (She’s worried about his health.)
Við höfum áhyggjur af veðrinu. (We’re worried about the weather.)

What exactly is því að? How is it different from af því að, þar sem, or vegna þess að?

All can introduce a reason, but there are nuances:

því að = “because.” Common in writing; neutral to slightly formal.
af því að = “because.” Extremely common in speech; fully standard.
þar sem = “since/as,” often when the reason is background/known.
vegna þess að = “because/due to the fact that,” heavier/formal. Important: því by itself usually means “therefore,” not “because,” so keep the að.

Do I need the comma before því að?

It’s customary (and safe) to put a comma before a causal clause introduced by því að or af því að:
Ég hef ekki áhyggjur, því að kennarinn hjálpar.
If you front the reason clause, put a comma after it: Af því að kennarinn hjálpar, hef ég ekki áhyggjur.

What word order do I use after því að? Can I say því að hjálpar kennarinn?

After a subordinator like því að / af því að, use normal subordinate-clause order: subject before the finite verb. So:

Correct: því að kennarinn hjálpar
Not standard: því að hjálpar kennarinn
(Inversion is for main clauses; subordinate clauses don’t do V2 in Icelandic.)

Shouldn’t hjálpar have an object (like “me”)?

Often, yes. Hjálpa typically takes a dative person:

Kennarinn hjálpar mér. (The teacher helps me.) To add what you’re being helped with:
hjálpa mér með verkefnið (with the assignment)
hjálpa mér við verkefnið (at/with the assignment)
hjálpa mér að læra (to study/learn)

Why is it kennarinn and not kennari?

Kennarinn is the definite form (“the teacher”), so the sentence refers to a specific teacher already known in context. Kennari is indefinite (“a teacher”). Icelandic marks definiteness with a suffix: kennari → kennarinn.

Could I say Ég hef engar áhyggjur?

Yes. Ég hef engar áhyggjur emphasizes “I have no worries at all.”
Ég hef ekki áhyggjur is a bit more neutral: “I’m not (particularly) worried.”

Is hef here the perfect auxiliary (like “I have done”)?

No. Here hef is the main verb hafa (“to have/possess”) in the idiom hafa áhyggjur. The perfect auxiliary use would be something like Ég hef lesið (“I have read”).

Can I put the because-clause first?

Yes, it’s grammatical, though leading with a reason is less common in very casual speech. For example:

Af því að kennarinn hjálpar, hef ég ekki áhyggjur.
Þar sem kennarinn hjálpar, hef ég ekki áhyggjur.
Keep the comma after the clause.

Are there other natural ways to say “I’m not worried”?

Yes:

Ég er ekki stressaður/stressuð. (I’m not stressed.)
Ég er rólegur/róleg. (I’m calm.)
Ég er áhyggjulaus/áhyggjulaus. (I’m worry-free.)
Choose endings that match your gender.

Any quick pronunciation tips for key words?

Approximate guide:

Ég ≈ “yeh” (often with a soft g-sound; many say it very quickly)
því ≈ “THVEE” (voiceless th as in “thing”)
að ≈ “ath” with a soft voiced th (as in “this”), very short
hjálpar ≈ “HYAU-l-par” (the hj is like a breathy h + y; á like “ow” in “cow”)
áhyggjur ≈ “OW-hig-yur” (stress on the first syllable)
kennarinn ≈ “KEN-na-rin” (r is tapped/trilled)