Jeg når ikke at læse bogen i aften.

Yes—nå literally relates to reaching, but in this sentence jeg når ikke at ... means I won’t manage to ..., I won’t get around to ..., or I won’t have time to ....

So:

• Jeg når ikke at læse bogen i aften = I won’t manage to read the book tonight
• Very natural English meaning: I won’t have time to read the book tonight

This is a very common Danish pattern:

• Jeg når at spise = I’ll manage to eat / I’ll have time to eat
• Vi når ikke toget = We won’t catch the train

So nå can mean different kinds of reaching: reaching a place, a deadline, or enough time to do something.

Because after nå in this structure, Danish normally uses at + infinitive.

Pattern:

• nå at + infinitive

Examples:

• Jeg når at spise = I’ll manage to eat
• Hun når ikke at komme = She won’t manage to come
• Vi nåede at se filmen = We managed to see the film

So in your sentence:

• læse = read
• at læse = to read

English often also uses to here, so the structure is fairly similar.

Because in a normal main clause, Danish places the finite verb early in the sentence, and sentence adverbs like ikke usually come after that finite verb.

Here:

• Jeg = subject
• når = finite verb
• ikke = not
• at læse bogen i aften = rest of the sentence

So:

• Jeg når ikke at læse bogen i aften

This is standard Danish word order.

Compare:

• Jeg kommer ikke i morgen = I’m not coming tomorrow
• Han kan ikke svømme = He cannot swim

The ikke usually follows the finite verb in main clauses.

Because Danish main clauses follow the verb-second principle, often called V2. That means the finite verb typically comes in the second position.

So the normal order is:

• Jeg når ikke at læse bogen i aften

Not:

• Jeg ikke når ...

A simple way to think about it:

• Subject first
• Finite verb second
• ikke usually after the finite verb

This is one of the most important word-order rules in Danish.

They are similar, but not identical.

• Jeg når ikke at læse bogen i aften = I won’t have enough time / I won’t manage to get it done tonight
• Jeg kan ikke læse bogen i aften = I can’t read the book tonight

Kan ikke is broader. It could mean:

• I don’t have time
• I’m not able to
• I’m not allowed to
• It’s not possible for some reason

Når ikke at specifically focuses on time/opportunity before it’s too late.

So if the problem is lack of time, når ikke at is often the better choice.

Actually, bogen already means the book.

In Danish, the definite article is usually attached to the end of the noun:

• en bog = a book
• bogen = the book

So:

• bog = book
• -en = the definite ending for a common-gender noun here

That is why Danish usually does not say a separate word for the in simple cases.

More examples:

• en bil = a car
• bilen = the car
• en stol = a chair
• stolen = the chair

Because i aften is the normal Danish expression for tonight / this evening.

• i aften = tonight / this evening
• literally, it looks like in evening, but you should learn it as a fixed time expression

Examples:

• Vi ses i aften = See you tonight
• Han arbejder i aften = He’s working tonight

So in your sentence:

• i aften tells you when the reading would happen

It can mean either, depending on context.

In many cases, English could translate it as:

• tonight
• this evening

For your sentence, both are possible:

• I won’t have time to read the book tonight
• I won’t have time to read the book this evening

If the context is later in the day, English often prefers tonight. But the Danish phrase itself is the normal one in both kinds of situations.

Because Danish often uses the present tense for future meaning when the time is clear from context.

Here, i aften makes the future time obvious:

• Jeg når ikke at læse bogen i aften

So even though når is present tense, the whole sentence refers to later today / tonight.

This is very common in Danish:

• Jeg kommer i morgen = I’m coming tomorrow
• Vi ses i aften = We’ll see each other tonight

English does something similar in some cases, though English often uses will more often than Danish does.

Normally, no. After nå in this meaning, Danish uses at + infinitive.

So the correct form is:

• Jeg når ikke at læse bogen i aften

Without at, it sounds ungrammatical to most speakers.

This is just one of those verb patterns you need to learn:

• some verbs take a bare infinitive
• some take at + infinitive

And nå in this structure takes at + infinitive.

Yes, that can work in English, especially in a more informal or context-based translation. It gives a similar idea of not managing to find the time/opportunity.

Possible translations include:

• I won’t have time to read the book tonight
• I won’t manage to read the book tonight
• I’m not going to get to read the book tonight

The best translation depends on tone:

• won’t have time = very natural everyday English
• won’t manage to = closer to the literal Danish structure
• won’t get to = emphasizes not having the chance

In a subordinate clause, Danish word order changes, and ikke usually comes before the finite verb.

Main clause:

• Jeg når ikke at læse bogen i aften

Subordinate clause:

• ... fordi jeg ikke når at læse bogen i aften
• ... because I won’t have time to read the book tonight

So this is a useful contrast:

• Main clause: jeg når ikke
• Subordinate clause: jeg ikke når

That difference is very important in Danish grammar.