Saken er viktig.

Because saken is the definite singular form of sak.

• sak = a case / a matter / an issue
• saken = the case / the matter / the issue

In Norwegian, the definite article is often added to the end of the noun as a suffix.

So:

• en sak = a case
• saken = the case

That is why Saken er viktig means The case/matter is important, not A case/matter is important.

The ending -en is the usual definite ending for many masculine nouns in Norwegian Bokmål.

Here:

• sak is a noun
• saken = sak + en

This works like the in English.

More examples:

• bil = car

• bilen = the car

• hund = dog
• hunden = the dog

So in this sentence, -en is doing the job that English the does.

Yes. Er means is / am / are, depending on context. It is the present tense of å være = to be.

Examples:

• Jeg er trøtt. = I am tired.
• Du er snill. = You are kind.
• Saken er viktig. = The matter is important.

Unlike English, Norwegian does not change the present-tense form of to be depending on the subject:

• jeg er
• du er
• han er
• vi er

So er is very convenient: it stays the same.

Because viktig agrees with a singular neuter pattern when used after er with this noun phrase structure? Not exactly—the simplest learner rule here is:

After er, adjectives are usually in their normal predicate form, and with a singular noun like saken, viktig is the correct form.

More specifically:

• en viktig sak = an important matter
• saken er viktig = the matter is important

The form viktige is usually used with:

• plural nouns: viktige saker = important matters
• definite nouns in front of the noun: de viktige sakene = the important matters
• some other specific adjective patterns

So in this sentence, viktig is the natural correct form.

Yes, in this sentence it is very similar to English:

• Saken = subject
• er = verb
• viktig = adjective/complement

So it follows the pattern:

Subject + verb + adjective

This makes Saken er viktig very straightforward for English speakers.

However, Norwegian often uses verb-second word order, so in other sentence types the order can change:

• Saken er viktig. = The matter is important.
• I dag er saken viktig. = Today, the matter is important.

Notice that when another element comes first, the verb still comes second.

A simple approximate pronunciation for an English speaker is:

SAH-ken er VIKH-tih

A few details:

• saken: the first syllable is stressed: SA-ken
• er is often pronounced very lightly in normal speech
• viktig has stress on the first syllable: VIK-
• the g in viktig is not pronounced like a strong English g at the end of a word

A rougher English-friendly version could be:

SAH-ken e(r) VIKH-ti

Pronunciation varies a bit by dialect, but that will be understood well.

Sak is a flexible word. Depending on context, it can mean:

• case
• matter
• issue
• sometimes even thing, in certain expressions

So Saken er viktig could be understood as:

• The case is important
• The matter is important
• The issue is important

Which translation sounds best depends on the situation:

• in law: the case
• in politics or discussion: the issue or the matter
• in general conversation: often the matter

Yes, but it means something different.

• En sak er viktig. = A matter/case is important.
• Saken er viktig. = The matter/case is important.

So the difference is the same as a vs the in English.

Usually, Saken er viktig sounds more natural if both speaker and listener already know which case or matter is being discussed.

You would change both the noun and the adjective:

• Sakene er viktige. = The matters/cases are important.

Breakdown:

• sakene = the matters / the cases
• er = are
• viktige = plural form of important

Compare:

• Saken er viktig. = The matter is important.
• Sakene er viktige. = The matters are important.

Yes. This is a very common Norwegian sentence pattern:

Definite noun + er + adjective

Examples:

• Boken er interessant. = The book is interesting.
• Maten er god. = The food is good.
• Filmen er lang. = The movie is long.
• Saken er alvorlig. = The matter is serious.

So Saken er viktig is a useful model sentence to learn from.