Learn Danish: Hun læser bogen mens han sover. - She reads the book while he sleeps.

mens means 'while' and acts as a subordinating conjunction. This means it introduces a dependent part of the sentence (han sover) that cannot stand alone and attaches it to the main action (Hun læser bogen).

The English translation uses 'reads' and 'sleeps'. Can this also mean 'is reading' and 'is sleeping'?

Yes! Danish does not have a separate '-ing' tense for ongoing actions. The present tense verbs læser and sover translate to both 'reads/sleeps' and 'is reading/is sleeping'. The context tells you it is happening right now.

Does using mens change the word order of the second half of the sentence?

Here, it looks like standard Subject-Verb order (han sover). However, because mens creates a subordinate clause, any small adverbs like ikke (not) or ofte (often) must be placed before the verb. For example: mens han ikke sover (while he is not sleeping).

Why is the word for book written as bogen here?

This is a quick reminder of how definite nouns work in Danish. To say 'the book', you take the base word bog (book) and attach the matching 'the' ending (-en) to the back, creating bogen.