Við lærum af mistökunum okkar.

Yes:

• Við = we
• lærum = learn; specifically, 1st person plural present tense of læra
• af = from
• mistökunum = the mistakes in the dative plural
• okkar = our

So grammatically, the structure is:

Við + lærum + af mistökunum okkar
= We learn from our mistakes

Lærum is the present tense, 1st person plural form of the verb læra (to learn).

A few present-tense forms are:

• ég læri = I learn
• þú lærir = you learn
• við lærum = we learn

So við lærum means we learn.

Because læra af is the normal Icelandic way to say learn from something or someone.

So:

• læra af mistökum = learn from mistakes
• læra af reynslunni = learn from experience
• læra af öðrum = learn from others

This is partly vocabulary and partly grammar: the verb læra often combines with af when the meaning is learn from.

Because af takes the dative case.

The noun mistök changes form after af:

• mistök = mistakes
• af mistökum = from mistakes
• af mistökunum = from the mistakes

So the ending -unum shows that the noun is:

• dative
• plural
• definite

In this sentence, -unum marks the noun as definite dative plural.

You can think of the forms like this:

• mistök = mistakes
• mistökum = mistakes, in the dative plural
• mistökunum = the mistakes, in the dative plural

So mistökunum is not a completely different word; it is the same noun with case and definiteness added.

Grammatically, mistök is normally a plural noun in modern Icelandic.

That is important, because learners often expect a singular form meaning a mistake, but Icelandic usually uses the plural-form noun mistök.

Useful forms:

• mistök = mistakes
• mistökum = mistakes (dative)
• mistaka = of mistakes

So in your sentence, mistökunum is the dative plural definite form of that plural noun.

Because that is a very common and natural way to place possessives in Icelandic.

So Icelandic often says:

• mistökin okkar = our mistakes
• húsið okkar = our house
• kennarinn okkar = our teacher

This post-noun possessive position is very normal.

English puts the possessive first: our mistakes.
Icelandic very often puts it after: mistökin okkar.

Because in Icelandic, a noun with a following possessive is very often definite.

So:

• mistökin okkar literally looks a bit like the mistakes our
• but it simply means our mistakes

This is standard Icelandic structure, not a mistake and not an odd double article.

In this sentence, because of af, that becomes:

• mistökunum okkar = from our mistakes

Yes, you can, but it is not quite the same in feel.

Compare:

• af mistökunum okkar = the most neutral, very natural way here
• af okkar mistökum = also possible, but often a bit more contrastive or emphatic, like from our mistakes rather than someone else’s

When the possessive comes before the noun, the noun usually does not take the definite ending.

So:

• af okkar mistökum is possible
• af okkar mistökunum is normally not the standard choice

No. Okkar stays okkar.

That is different from some other Icelandic possessives, such as minn / mín / mitt, which do change.

So you get:

• húsið okkar = our house
• bíllinn okkar = our car
• bækurnar okkar = our books
• af mistökunum okkar = from our mistakes

The noun changes, but okkar does not.

The sentence as given is the most neutral order:

Við lærum af mistökunum okkar.

But Icelandic word order can change for emphasis, while still following the language’s verb-second pattern.

For example:

• Af mistökunum okkar lærum við.

That version emphasizes from our mistakes more strongly.

So the original sentence is the straightforward, neutral way to say it, but other orders are possible depending on focus.

In a normal statement, you usually include við.

So:

• Við lærum af mistökunum okkar. = normal full statement

If you say only:

• Lærum af mistökunum okkar

that sounds more like:

• Let’s learn from our mistakes
• or a shortened, context-dependent phrase

So for the plain meaning we learn from our mistakes, við is the normal subject to use.