Learn Hardcore Icelandic: Í listasafninu lærir stelpan ný orð í dagbókina sína í stað þess að leiðast. - In the art museum the girl learns new words for her diary instead of being bored.

In Icelandic main clauses, the finite verb is almost always in second position in the sentence, no matter what comes first. This is called V2 word order.

Here, Í listasafninu (“in the art museum”) is moved to the front for emphasis.
Because that takes the first position, the verb lærir (“learns”) has to be second.
The subject stelpan (“the girl”) then comes after the verb.

So the underlying neutral order could be thought of as:

Stelpan lærir ný orð… – “The girl learns new words…”

But when you front Í listasafninu, the V2 rule forces:

Í listasafninu lærir stelpan ný orð…

What is going on with Í listasafninu? Why the ending -inu, and what case is this?

Listasafn means “art museum” (literally “art-collection”). Icelandic doesn’t use a separate word for “the”; instead it adds a definite ending to the noun.

listasafn = art museum (indefinite)
listasafnið = the art museum (nom/acc sg)
listasafni = art museum (dative sg, indefinite)
listasafninu = the art museum (dative sg, definite)

The preposition í (“in”) here expresses location, so it takes the dative case:

í
- dative → í listasafninu = “in the art museum”

So -inu is the definite article in the dative singular.

Why is it stelpan and not just stelpa for “the girl”? Where is the word “the”?

Icelandic usually does not have a separate word for “the”. Instead, “the” is expressed by an ending attached to the noun:

stelpa = (a) girl
stelpan = the girl
stelpu = (a) girl (acc./dat. sg.)
stelpuna = the girl (acc. sg.)
stelpunni = the girl (dat. sg.)

Here, stelpan is in the nominative singular definite: it’s the subject and it means “the girl”.

Why is there no “the” or “a” in ný orð? Shouldn’t it be something like “the new words”?

Icelandic doesn’t have an indefinite article (“a / an”) at all, and it uses the definite suffix for “the”. Since ný orð has no definite ending, it stays just “new words” without any article.

ný = “new” (neuter plural nominative/accusative form here)
orð = “word / words” (neuter; nom./acc. singular and plural look the same)

If you wanted “the new words”, you would say:

hin nýju orð or nýju orðin = “the new words”

In this sentence, ný orð is just indefinite plural: “new words”.

How do I know orð is plural here, since the singular and plural look the same?

You’re right: for neuter nouns like orð, the nominative and accusative singular and plural often look identical.

We know it’s plural here mainly from:

The meaning: “learn new word” is odd; “learn new words” is natural.
The adjective ný is in the neuter plural form (nom./acc. plural neuter is ný; singular neuter would be nýtt if it were definite, e.g. hið nýja orð).

So grammatically:

ný orð = “new words” (neuter plural accusative here, object of lærir).

Why is it í dagbókina and not í dagbókinni? What’s the difference?

The preposition í can take either accusative or dative, with a change in meaning:

í + dative → location (“in, inside” – static)
í + accusative → movement or putting something into something (“into” – dynamic)

Compare:

Hún situr í dagbókinni. = She is sitting in the diary (nonsense, but grammatically: static, dative).
Hún skrifar í dagbókina. = She writes into the diary (dynamic, accusative).

In the sentence, í dagbókina sína suggests the words are being put into her diary (conceptually like “into her diary”), so accusative is used:

dagbók = diary
dagbókina = the diary (accusative singular definite)
í dagbókina = into the diary

What does sína do in í dagbókina sína? How is it different from hennar?

Sína is the reflexive possessive pronoun (feminine, accusative singular here). It always refers back to the subject of the same clause.

dagbókina sína = her own diary (the diary of stelpan, the girl)

If you used hennar:

dagbókina hennar can mean “her diary” but not necessarily the subject’s. It could be some other woman’s diary, depending on context.

So in this sentence:

dagbókina sína clearly means the diary belonging to the girl mentioned as subject.
Grammatically: dagbókina (f, acc. sg. definite) + sína (f, acc. sg. reflexive) agree in gender, number, and case.

How does the structure í stað þess að leiðast work? What does each word contribute?

Í stað þess að + infinitive is a very common Icelandic pattern meaning “instead of doing X”.

Breakdown:

í stað = “in place (of), instead”
þess = genitive neuter pronoun “of that / of it”
Together í stað þess ≈ “instead of that”
að leiðast = “to be bored” (infinitive of leiðast)

Literally: “in place of that to be bored”, but idiomatically:

í stað þess að leiðast = “instead of being bored”

You can swap in other verbs:

í stað þess að sofa = instead of sleeping
í stað þess að lesa = instead of reading

Why is the verb leiðast used here, and why does it have -st at the end?

Leiðast is a so‑called -st verb, often called a “middle” or “reflexive-like” form. It commonly means “to be bored”.

In normal usage it’s impersonal with a dative experiencer:

Mér leiðist. = I am bored. (Literally “It bores to me.”)
Honum leiðist. = He is bored.
Krökkunum leiðist. = The kids are bored.

The infinitive of this verb is leiðast, and after að you always use the infinitive:

að leiðast = to be bored

So í stað þess að leiðast is grammatically parallel to English “instead of being bored”, even though Icelandic uses a special -st form.

What form is lærir, and how would the verb læra conjugate?

Lærir is:

3rd person
singular
present tense
of the verb að læra (“to learn”).

Very roughly:

Ég læri – I learn
Þú lærir – you learn (sg.)
Hann / hún / það lærir – he / she / it learns
Við lærum – we learn
Þið lærið – you (pl.) learn
Þeir / þær / þau læra – they learn

So stelpan lærir = “the girl learns”.

Which words are in which cases in this sentence, and why?

Main elements and their cases:

stelpan – nominative singular definite
→ Subject of the verb lærir.
ný orð – accusative plural (neuter)
→ Direct object of lærir (“learns what?” → new words).
í listasafninu – dative singular definite
→ Object of the preposition í expressing location, which takes dative.
í dagbókina sína – accusative singular definite (for dagbókina), with sína agreeing in gender/number/case
→ Object of í expressing movement into / putting into, which takes accusative.
í stað þess – genitive (þess is genitive neuter) after the fixed phrase í stað (þess)
→ Part of the idiom “instead of”.

Icelandic heavily marks these roles with case endings rather than relying only on word order.

Could I change the word order, for example say Stelpan lærir ný orð í dagbókina sína í listasafninu? Is that still correct?

Yes, that word order is also grammatically correct, and may even sound more neutral in some contexts:

Stelpan lærir ný orð í dagbókina sína í listasafninu.

Differences:

Your version keeps the subject stelpan first, which feels a bit closer to English style.
The original Í listasafninu lærir stelpan… puts “in the art museum” in the first position for emphasis on the location.

Both respect the main rule that the finite verb is in second position in the clause:

Stelpan (1) lærir (2) ný orð…
Í listasafninu (1) lærir (2) stelpan…

The rest of the phrase order (where you put the prepositional phrases about diary and museum) is fairly flexible and mainly affects emphasis or rhythm, not grammaticality.