Learn Hardcore Icelandic: Hún vill læra á annað hljóðfæri í framtíðinni. - She wants to learn another instrument in the future.

Hún – she
vill – wants (3rd person singular of vilja, to want)
læra – to learn (infinitive)
á – on / to (on), here part of the idiom læra á
annað – another / a second (neuter form of annar)
hljóðfæri – musical instrument
í – in
framtíðinni – the future (literally: in the future, with a definite ending and dative case)

Why is it vill and not vil or something else?

Vill is the correct 3rd person singular present form of vilja (to want).

Present tense of vilja:

ég vil – I want
þú vilt – you (sg.) want
hann/hún/það vill – he/she/it wants
við viljum – we want
þið viljið – you (pl.) want
þeir/þær/þau vilja – they want

Because the subject is Hún (she), you must use vill.

What is the role of læra here, and why is it in this form?

Læra is the infinitive form of the verb to learn.

In Icelandic, when you use vilja (want) followed by another verb, that second verb stays in the infinitive:

Hún vill læra – She wants to learn.
Ég vil borða – I want to eat.

So læra is not conjugated for person or tense here; vill carries the tense/person, and læra is just the infinitive.

Why do we say læra á when talking about a musical instrument?

The combination læra á + [object] is an idiomatic structure that often means learn to use/play/operate [something]. With instruments it essentially means learn to play that instrument.

Typical uses:

læra á píanó – learn (to play) the piano
læra á gítar – learn (to play) the guitar
læra á bíl – learn to drive a car
læra á tölvu – learn how to use a computer

You could say just læra hljóðfæri, but that sounds more like learn (about) an instrument in a theoretical sense. Læra á hljóðfæri is the natural way to express learn to play an instrument.

What case is annað hljóðfæri in, and why?

Á can take either accusative or dative depending on meaning. With this “target/affected thing” meaning (as in playing or learning an instrument), it takes the accusative.

annað – neuter accusative singular of annar (other/another)
hljóðfæri – neuter noun; nominative and accusative singular look the same

So á annað hljóðfæri is a prepositional phrase with á + accusative, describing what she is learning to play.

Why is it annað and not annar or aðra?

Annar is an adjective/pronoun meaning other, another, second. It must agree in gender, number, and case with the noun hljóðfæri.

Hljóðfæri is neuter, singular, accusative here.
The neuter nominative/accusative singular form of annar is annað.

Main forms in the nominative singular:

masculine: annar
feminine: önnur
neuter: annað

Accusative singular:

masculine: annan
feminine: aðra
neuter: annað (same as nominative)

So annað hljóðfæri is the correct neuter accusative singular agreement.

What kind of word is hljóðfæri, and how does it decline?

Hljóðfæri is a neuter noun meaning musical instrument.

Singular:

nom: hljóðfæri
acc: hljóðfæri
dat: hljóðfæri
gen: hljóðfæris

Plural:

nom: hljóðfæri
acc: hljóðfæri
dat: hljóðfærum
gen: hljóðfæra

Notice that in the singular, nominative/accusative/dative all look the same; the genitive adds -s. The plural adds -um in the dative and -a in the genitive.

Why is framtíðinni in the definite form (the future) instead of just framtíð?

Icelandic usually says í framtíðinni literally in the future-the where English just says in the future. This is a standard idiomatic way to talk about the future in general.

framtíð – future
framtíðin – the future (nominative)
framtíðinni – the future (dative)

Since the preposition í here expresses location in time (in the future), it takes dative, and the definite dative singular of framtíð is framtíðinni.

So í framtíðinni = in the future.

Why does í take the form framtíðinni (dative) here?

The preposition í (in, into) can take either:

accusative – when there is movement into/into a new state
dative – when it’s location or time in/inside/within

Here it means in the future (a time span, not movement into something), so í governs the dative:

í framtíðinni – in the future (dative)
Compare: í hús (acc.) – into the house vs í húsinu (dat.) – in the house

Can the word order change, for example Hún vill í framtíðinni læra á annað hljóðfæri?

Yes, that is possible and grammatical. Both are fine:

Hún vill læra á annað hljóðfæri í framtíðinni.
Hún vill í framtíðinni læra á annað hljóðfæri.

The default, most neutral order puts time phrases like í framtíðinni at the end. Moving í framtíðinni earlier can add slight emphasis on the time frame, but the basic meaning is the same.

Does Icelandic have a special future tense? Why is everything in the present even though we say “in the future”?

Icelandic normally uses the present tense with a future meaning when the context makes it clear, often with time expressions like:

á morgun – tomorrow
næsta ár – next year
í framtíðinni – in the future

So:

Hún vill læra á annað hljóðfæri í framtíðinni.
– literally: She wants to learn on another instrument in the future.

You could use other verbs to make a future-ish sense (ætla – intend to, munu – a future auxiliary), but a distinct future tense like in English does not exist. Present + a time expression is very normal.

How would I say “She would like to learn another instrument in the future” instead of “She wants”?

A natural, slightly softer version in Icelandic is to use langar instead of vill:

Hana langar til að læra á annað hljóðfæri í framtíðinni.

Breakdown:

Hana – her (accusative; with langar the person is in accusative)
langar – would like / feels like (3rd sg. of langar)
til að læra – to learn
á annað hljóðfæri í framtíðinni – same as before

Semantically this is close to English would like to, a bit less direct than Hún vill….