Jeg vil følge et kursus i engelsk på universitetet.

Jeg vil følge means I want to / will attend / am going to take. The verb vil is a modal verb, and here it often expresses intention or desire.

• Jeg følger et kursus = I am attending / I attend a course
• Jeg vil følge et kursus = I want to attend / I am going to take a course

So vil changes the meaning from a simple statement to something more about intention.

Yes, følge often does mean follow, but in this context it means to attend or to take a course.

So:

• at følge et kursus = to attend / take a course

This is a very natural Danish expression, even though English would usually not say follow a course in the same way.

Because kursus is a neuter noun in Danish, so it takes et in the indefinite singular.

• et kursus = a course
• kurset = the course

In Danish, nouns are mainly divided into two grammatical genders:

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

You usually have to learn the article together with the noun.

After a modal verb like vil, Danish uses the bare infinitive, just like English often does.

• Jeg vil følge = I want to / will attend
• compare English: I will attend, not I will to attend

Common Danish modal verbs that work like this include:

• vil = want to / will
• kan = can
• skal = shall / must / am supposed to
• må = may / must
• bør = should

So vil følge is completely normal.

Here i engelsk means in English in the sense of in the subject of English.

• et kursus i engelsk = a course in English / an English course as a subject

By contrast, på engelsk usually means in the English language.

For example:

• Jeg læser engelsk. = I study English.
• Et kursus i engelsk = a course in English (the subject)
• Undervisningen foregår på engelsk. = The teaching takes place in English

So:

• i engelsk = about the subject
• på engelsk = using the English language

Danish often uses på with institutions and places of study, where English might use at.

• på universitetet = at the university
• på skolen = at school
• på hospitalet = at the hospital in some contexts

So på universitetet is the natural Danish way to say at the university.

Because that is the definite form of the neuter noun universitet.

• et universitet = a university
• universitetet = the university

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

• en bog → bogen
• et hus → huset
• et universitet → universitetet

So på universitetet literally means at the university.

The basic order is:

Jeg + vil + følge + et kursus i engelsk + på universitetet

That is:

• Jeg = subject
• vil = finite verb
• følge = infinitive
• et kursus i engelsk = object
• på universitetet = place expression

This is standard Danish main-clause word order: the finite verb usually comes in the second position.

Yes. Tage et kursus is also very natural and may sound especially familiar to English speakers because it is close to take a course.

Both are possible:

• følge et kursus = attend/follow a course
• tage et kursus = take a course

Depending on context, one may sound slightly more formal or more common, but both are good Danish.

No. In Danish, names of languages are normally not capitalized.

So:

• engelsk
• dansk
• tysk

This is different from English, where English, Danish, and German are capitalized.

Yes, and that can be confusing for learners. Vil can express:

• future meaning: will
• desire/intention: want to

In many everyday sentences, the distinction depends on context.

For example:

• Jeg vil spise nu. could mean I want to eat now or sometimes I will eat now, depending on the situation.

In your sentence, Jeg vil følge et kursus i engelsk på universitetet, the most natural interpretation is often I want to take / I am going to take an English course at the university.

Yes. Danish often moves elements to the front for emphasis, but then the finite verb must still stay in second position.

For example:

• På universitetet vil jeg følge et kursus i engelsk.

This puts more emphasis on på universitetet.

Notice that when På universitetet comes first, vil still stays in the second position, and jeg comes after it. This is a very important Danish word-order rule.