Hun tager sin lille taske med til universitetet.

Because sin is the reflexive possessive form. Danish uses sin/sit/sine when the owner is the same as the subject of the sentence.

Here, the subject is Hun and the bag belongs to her, so Danish uses sin:

• Hun tager sin taske med = she takes her own bag along

If you said hendes, it would usually mean the bag belongs to another female person, not the subject:

• Hun tager hendes taske med = she takes her bag, meaning someone else’s bag

This is one of the biggest differences from English, since English uses her for both meanings.

Tage med is a very common Danish verb expression meaning take along or bring.

In Danish main clauses, some verb expressions split up like this:

• Hun tager sin lille taske med
• infinitive: at tage en taske med

So tager is the verb, and med is a particle that belongs with it.

A useful comparison:

• tage = take
• tage med = take along / bring

You will often see this kind of split word order in Danish.

Because tager is the present tense of at tage.

• at tage = to take
• tager = take / takes / am taking / is taking, depending on context

Danish present tense is usually formed by adding -r to the infinitive:

• at bo → bor
• at læse → læser
• at tage → tager

So Hun tager simply means she takes or she is taking, depending on the situation.

Yes. Lille is the normal adjective form here, and it is a bit irregular compared with many other Danish adjectives.

With a noun like taske:

• en stor taske = a big bag
• en lille taske = a small bag

So you just learn lille as the form used before the noun.

It is very common, and you do not say en lil taske in standard written Danish.

Because sin already functions as the determiner.

In Danish, just like in English, you normally do not combine a possessive with an indefinite article:

• sin lille taske = her small bag
• not sin en lille taske

Compare English:

• her bag
• not her a bag

So sin takes the place where en would otherwise go.

Because universitetet is the definite form of universitet.

• et universitet = a university
• universitetet = the university

Danish usually puts the definite article at the end of the noun:

• bogen = the book
• huset = the house
• universitetet = the university

So the -et means the.

Because til shows movement toward a destination, while på usually shows location.

• Hun tager sin lille taske med til universitetet = she is going to the university
• Hun er på universitetet = she is at the university

So:

• til = to, toward
• på = on / at, depending on context

This is a very common distinction in Danish.

Yes. In natural English, tage med is often translated as either take along or bring, depending on perspective.

So this sentence could sound natural in English as:

• she takes her small bag with her to the university
• she brings her small bag to the university

Danish often does not force the same take/bring distinction that English does in every context. The important idea is that she is bringing it along with her.