Learn Hardcore Icelandic: Sjálfstraustið er mjög mikilvægt í lífinu. - Self-confidence is very important in life.

In Icelandic, the definite article is usually a suffix, not a separate word like the in English. For neuter nouns in the nominative singular, that ending is -ið (or sometimes just -ð if the noun already ends in i).

So sjálfstraustið literally means “the self‑confidence”, even though in English we normally just say “self‑confidence” without the in a sentence like this.

Could I say Sjálfstraust er mjög mikilvægt í lífinu without the -ið? Would that be wrong or change the meaning?

You can say Sjálfstraust er mjög mikilvægt í lífinu, and it is grammatically correct. The difference is subtle:

Sjálfstraustið er mjög mikilvægt í lífinu.
Uses the definite form. This is the most natural way to make a general statement about this concept:
“Self‑confidence (as a thing, this quality) is very important in life.”
Sjálfstraust er mjög mikilvægt í lífinu.
Uses the indefinite form. This also works, and still sounds like a general statement, but it can feel a bit more like “having self‑confidence / some self‑confidence is important in life.”

In practice, Icelandic often uses the definite form with abstract nouns when making broad, general statements, so sjálfstraustið is slightly more idiomatic here.

Why does mikilvægt end in -t? Why not something like mikilvægur?

The -t ending is there because mikilvægt is an adjective agreeing with a neuter noun.

Dictionary form: mikilvægur (masculine, nominative singular)
Feminine: mikilvæg
Neuter: mikilvægt

In this sentence, the subject sjálfstraustið is a neuter noun in the nominative singular, so the adjective that describes it must also be neuter nominative singular:

sjálfstraustið (neuter, nom. sg.)
mikilvægt (neuter, nom. sg.)

So you get: Sjálfstraustið er mjög mikilvægt í lífinu.
Using mikilvægur here would be incorrect, because that form is masculine.

What is the role of mjög in the sentence, and why doesn’t it change its form?

Mjög means “very” and is an adverb, not an adjective.

Adjectives (like mikilvægur / mikilvæg / mikilvægt) change their form to agree with the noun in gender, number, and case.
Adverbs like mjög do not change their form. They stay the same no matter what they modify.

Here, mjög modifies the adjective mikilvægt:

mikilvægt = important
mjög mikilvægt = very important

So mjög is invariable; you use mjög in all contexts.

What exactly is lífinu? What case and form is it, and why is it used here?

Lífinu is the dative singular definite form of líf (life), which is a neuter noun.

Rough declension of líf:

Nominative: líf – life
Accusative: líf
Dative: lífi
Definite dative: lífinu – the life

The preposition í (“in”) can take either:

Dative for location / state: in, inside (where?)
Accusative for movement into: into (where to?)

Here it means being in life in general, a kind of state or situation. That’s why it takes the dative:

í lífinu = “in (the) life” → idiomatically: in life

So grammatically:

í
- lífinu (dative sg. definite) = in life

Why is it í lífinu and not just í lífi or í líf?

Three different options and how they feel:

í lífinu
- Dative, definite: “in the life”
- This is the normal idiomatic way to say “in life” in a general sense.
- Used for broad statements:
  - Sjálfstraustið er mjög mikilvægt í lífinu.
    “Self‑confidence is very important in life.”
í lífi
- Dative, indefinite.
- This can be used in other contexts (e.g. “in [someone’s] life”, “in life” in a narrower, more specific sense), but for this kind of generic proverb‑like sentence, í lífinu is more natural.
í líf
- Accusative, indefinite. With í, that tends to imply movement into life, not a static situation, so it doesn’t fit the meaning here.

So í lífinu is chosen because:

í requires dative for a static “in” meaning, and
The definite form is the idiomatic choice for this kind of general statement.

Can the word order be different, for example Í lífinu er sjálfstraustið mjög mikilvægt?

Yes, Icelandic word order is flexible enough that you can move things around for emphasis.

Neutral, most typical order:
Sjálfstraustið er mjög mikilvægt í lífinu.
(Subject – verb – complement – adverbial phrase)
Emphasizing “in life”:
Í lífinu er sjálfstraustið mjög mikilvægt.
This is also correct. It puts í lífinu at the start, giving it more prominence:
“In life, self‑confidence is very important.”

Both are correct; the first sounds more neutral, the second slightly more emphatic or stylistic.

What does sjálfstraust literally consist of? Is it a compound word?

Yes, sjálfstraust is a compound noun:

sjálf = self
traust = trust, confidence

Put together:

sjálftraust / sjálfstraust = self‑trust → self‑confidence

Then with the definite suffix:

sjálfstraustið = “the self‑confidence”

How do you pronounce Sjálfstraustið er mjög mikilvægt í lífinu?

Approximate, English‑friendly guidance (I’ll break it up word by word):

Sjálfstraustið
- sj = like sh in shoe
- á = like ow in cow, but shorter and tenser
- lfstr = all pronounced, but the f and s can blend a bit
- au (in traust) = something like uh‑ee blended together
- ið = short i (as in bit) plus a soft ð like th in this
  Very roughly: SHYOLF‑strohyst‑ith (with stress on Sjálf‑)
er
- Similar to air, but shorter and crisper.
mjög
- mj = my but with the lips rounded right away
- ö = like German ö or French eu in peur
- Final g is a soft sound, often more like a soft gh than a hard g
  Roughly: myœg (one syllable)
mikilvægt
- mi as in mi of minimum
- kil like kill, but lighter; the k is often slightly palatal
- væ with æ like English eye
- gt is often reduced; you may mostly hear the k/t at the end
  Roughly: MI‑kil‑vaykt (stress on MI‑)
í lífinu
- í = like long ee in see
- lí = long lee
- fi = fi in fill (short i)
- nu = nu in nut (but with Icelandic u, somewhere between u and oo)
  Roughly: ee LEE‑fi‑nu

Main points:

Stress is almost always on the first syllable of each word.
Icelandic consonant clusters are often fully pronounced, but natives say them very smoothly and quickly.

What is the literal, word‑for‑word breakdown of the sentence?

Word by word:

sjálfstraustið = the self‑confidence
- sjálf = self
- traust = trust, confidence
- -ið = the (neuter, singular)
er = is (3rd person singular of að vera = to be)
mjög = very
mikilvægt = important (neuter form of the adjective)
- literally something like “of much weight/importance”
í = in
lífinu = the life (dative singular definite of líf)
→ idiomatically just “in life”

So, literally:
“The self‑confidence is very important in the life.”
Which corresponds in natural English to:
“Self‑confidence is very important in life.”