Í september byrjar hún á nýju námskeiði, og í október þarf hún ekki bara að lesa mikið, heldur líka að skrifa fleiri glósur.

Í is the normal preposition for in with months.

• í september = in September
• í október = in October

So this is just the regular Icelandic way to place something in a particular month.

This is because Icelandic main clauses usually follow the verb-second rule.

That means:

• the first element can be a time phrase, place phrase, object, etc.
• the finite verb still comes in the second position

So:

• Í september byrjar hún ...
• Í október þarf hún ...

The time phrase comes first, then the verb, then the subject hún.

Icelandic does not have a separate indefinite article like English a/an.

So nýtt námskeið or, here, nýju námskeiði can simply mean a new course.
Indefiniteness is usually understood from context.

If Icelandic wants to say the course, it normally marks definiteness on the noun itself, for example námskeiðið or in dative námskeiðinu.

The phrase byrja á e-u takes the dative.

So:

• dictionary form: námskeið = course
• dative singular: námskeiði

The adjective has to agree with the noun, so:

• nýju námskeiði = new course in dative singular neuter

So á nýju námskeiði is dative because of the construction byrja á.

Because it has to match námskeiði in:

• gender: neuter
• number: singular
• case: dative

The noun námskeið is neuter, and here it is in the dative singular, so the adjective appears as nýju.

The verb þurfa normally uses að + infinitive.

So:

• þarf að lesa = needs to read
• þarf að skrifa = needs to write

In the sentence, þarf is the finite verb, and lesa and skrifa are infinitives introduced by að.

This is the standard Icelandic pattern for not only ..., but also ...

So:

• ekki bara að lesa mikið
• heldur líka að skrifa fleiri glósur

means:

• not only to read a lot
• but also to write more notes

A useful thing to remember is that heldur commonly appears after a negative element such as ekki.

Here mikið means a lot.

It is the neuter singular form of mikill, but Icelandic often uses that form adverbially:

• vinna mikið = work a lot
• sofa mikið = sleep a lot
• lesa mikið = read a lot

So mikið is not describing a noun here; it is modifying the action lesa.

Use fleiri with countable plural nouns.

• fleiri glósur = more notes
• fleiri bækur = more books

Use meiri/meira for uncountable or mass quantity:

• meira vatn = more water
• meiri vinna = more work

Since glósur are individual countable items, fleiri is the correct choice.

Glósur is the plural of glósa, meaning note.

In this sentence it is the direct object of skrifa, so grammatically it is accusative plural. For this noun, the nominative plural and accusative plural happen to look the same:

• singular: glósa
• plural: glósur

So skrifa fleiri glósur means write more notes.