I mars vill jag börja en ny kurs i svenska.

Swedish often puts a time expression first when the speaker wants to set the scene or emphasize when something will happen.

So:

• I mars vill jag börja en ny kurs i svenska. = emphasis on In March
• Jag vill börja en ny kurs i svenska i mars. = more neutral, starting with I want...

Both are grammatical. The version with I mars first sounds very natural.

This is because Swedish follows the V2 rule in main clauses. V2 means the finite verb must come in the second position.

In this sentence:

• 1st position: I mars
• 2nd position: vill
• then the subject: jag

So:

• I mars vill jag börja... ✓
• I mars jag vill börja... ✗

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

Yes. With months, Swedish normally uses i.

Examples:

• i mars = in March
• i april = in April
• i december = in December

So this works much like English in March.

Because börja comes after vill, and after vill you use the infinitive form of the verb.

So:

• vill = want
• börja = to begin / begin

This is the same pattern as in English:

• I want to begin

In Swedish, modal verbs like vill, kan, måste, ska are followed by the bare infinitive:

• Jag vill börja
• Jag kan börja
• Jag måste börja

Not börjar.

Because kurs is an en-word in Swedish.

That affects both the article and the adjective:

• en = the article for common-gender nouns
• ny = the adjective form used with an en-word in singular indefinite form

So:

• en ny kurs = a new course

Compare:

• en ny bok
• en ny stol

If the noun were an ett-word, the adjective would usually change:

• ett nytt hus

But kurs is en kurs, so en ny kurs is correct.

Because en is the indefinite article, meaning a/an.

So:

• en ny kurs = a new course
• den nya kursen = the new course

Here the speaker is not talking about one specific already-known course, just some new course.

Here, svenska is a noun meaning the Swedish language.

So en kurs i svenska means:

• a course in Swedish
• a Swedish-language course, in the sense of studying the language itself

Swedish language names often look the same as adjectives, so context matters.

For example:

• svenska = Swedish / the Swedish language
• en svensk bok = a Swedish book

In your sentence, svenska means the language.

This is an important distinction.

• en kurs i svenska = a course in Swedish as a subject
  
  • You are studying the Swedish language.
• en kurs på svenska = a course taught in Swedish
  
  • The language of instruction is Swedish.

So in your sentence, i svenska is correct because it means the subject being studied is Swedish.

Yes, absolutely. That is also correct.

Compare:

• I mars vill jag börja en ny kurs i svenska.
• Jag vill börja en ny kurs i svenska i mars.

The difference is mainly emphasis:

• I mars... puts focus on the time
• Jag vill... puts focus on the speaker’s wish

Both are natural Swedish.

Because in Swedish, months and languages are normally written with lower-case letters.

So:

• mars not Mars
• svenska not Svenska

This is different from English, where March and Swedish are capitalized.

Both can be used, and learners often notice both patterns.

• börja en kurs = begin a course
• börja på en kurs = start taking a course

In everyday Swedish, börja på en kurs is very common. But börja en ny kurs is also possible and natural.

So your sentence is fine as it is. A slightly different but also very natural version would be:

• I mars vill jag börja på en ny kurs i svenska.

The meaning is almost the same.