Han løb for hurtigt i går og har nu et hævet knæ efter en skade.

Løb is the simple past form of the verb at løbe (to run).

• at løbe = to run
• løber = runs / is running
• løb = ran
• har løbet = has run

So Han løb ... i går means he did the running yesterday, at a finished time in the past.

That is a very common question. In Danish, for can mean different things depending on context.

In for hurtigt, for means too:

• for hurtigt = too fast
• for dyrt = too expensive
• for sent = too late

So here:

• Han løb for hurtigt = He ran too fast

But in other contexts, for can still mean for, as in:

• en gave til dig = a gift for you
• jeg gør det for ham = I do it for him

So you have to learn for + adjective/adverb as a very common pattern meaning too ....

In Danish, i går is the fixed expression for yesterday.

• i går = yesterday
• i dag = today
• i morgen = tomorrow

You should learn i går as a set phrase. You normally do not say just går for yesterday in modern standard Danish.

Because Danish usually prefers the simple past when the time is clearly finished and stated, especially with something like i går (yesterday).

So Danish normally says:

• Han løb i går = He ran yesterday

rather than:

• Han har løbet i går ❌

A good rule:

• use simple past with a definite finished time such as i går, sidste uge, i 2020
• use present perfect when the connection to the present matters and no finished past time is given

That is why the first part is Han løb ... i går.

Here har means has in the ordinary sense of possession/state:

• har nu et hævet knæ = now has a swollen knee

So this is not really a perfect tense like has run. It is the present-tense verb har plus a noun phrase:

• har = has
• nu = now
• et hævet knæ = a swollen knee

The sentence moves from a past event (he ran too fast yesterday) to a present result (and now he has a swollen knee).

Because knæ is a neuter noun in Danish, so its indefinite article is et, not en.

• et knæ = a knee
• knæet = the knee

Danish nouns are usually either:

• en-words (common gender)
• et-words (neuter)

Since knæ is an et-word, you must say:

• et hævet knæ

Because adjectives in Danish change form depending on the noun they describe.

Here the noun is:

• knæ = a neuter singular noun
• indefinite: et knæ

With a neuter singular indefinite noun, the adjective usually takes -t:

• et hævet knæ = a swollen knee
• et stort hus = a big house
• et rødt æble = a red apple

Compare:

• en hævet arm = a swollen arm
• et hævet knæ = a swollen knee
• det hævede knæ = the swollen knee

So the -t is there because knæ is neuter singular indefinite.

It is functioning as an adjective here, even though historically it comes from a participle form.

In practice, for learners, the important thing is that in this sentence it behaves like an adjective describing knæ:

• et hævet knæ = a swollen knee

You can think of it the same way you think of English adjectives like swollen, tired, or broken, which also come from participle forms but work as adjectives.

Because Danish often leaves out the repeated subject in the second part of a coordinated sentence when it is clearly the same subject.

So:

• Han løb for hurtigt i går og har nu et hævet knæ ...

means the same subject is understood in both parts:

• Han løb ... og (han) har nu ...

You could also say:

• Han løb for hurtigt i går, og han har nu et hævet knæ ...

but repeating han is not necessary here.

Because the second clause is continuing with the same understood subject, so the verb comes first in what is effectively a shortened coordinated clause:

• ... og har nu et hævet knæ

If you explicitly included the subject, you could say:

• ... og han har nu et hævet knæ

If you put nu first, then you would normally need inversion with an expressed subject:

• ... og nu har han et hævet knæ

So og har nu ... is natural because han is omitted but still understood.

Nu means now. It shows the present result of the earlier action.

So the structure is:

• past event: Han løb for hurtigt i går
• present consequence: og har nu et hævet knæ

It helps connect the two ideas: he ran too fast yesterday, and now the result is that his knee is swollen.

Literally, it means after an injury or following an injury.

In context, it gives background for why the knee is swollen. Depending on context, English might translate it as:

• after an injury
• following an injury
• sometimes even from an injury

So it describes the situation or cause connected to the swollen knee.

Because skade is a countable noun, and here it means an injury, so Danish uses the indefinite article:

• en skade = an injury

Just skade without an article would usually not work in this sentence.

Also, skade is an en-word:

• en skade
• skaden

So the phrase is:

• efter en skade = after an injury

Here it is an adverb, because it describes how he ran.

• hurtig = fast, quick (adjective)
• hurtigt = fast / quickly (adverb form)

Examples:

• en hurtig bil = a fast car
• Han løber hurtigt = He runs fast / quickly

So in Han løb for hurtigt, hurtigt describes the verb løb.

Yes. In English, both may work depending on style and context.

• Han løb hurtigt = He ran fast / He ran quickly

And with for:

• Han løb for hurtigt = He ran too fast

English usually sounds more natural with too fast here, even though too quickly is also possible.

It has two coordinated parts joined by og (and):

1. Han løb for hurtigt i går

   • subject: Han
   • verb: løb
   • adverb phrase: for hurtigt
   • time phrase: i går

2. (Han) har nu et hævet knæ efter en skade

   • understood subject: (Han)
   • verb: har
   • time adverb: nu
   • object/noun phrase: et hævet knæ
   • extra phrase: efter en skade

So the sentence moves very naturally from past action to present consequence.