Kennarinn notar nýja kennslubók í íslensku.

The ending -inn is the definite article attached to the noun.

• kennari = teacher
• kennarinn = the teacher

In Icelandic, the word for the is not separate like in English; it is usually added as a suffix to the noun:

• stóll = chair → stól
  • inn = stólinn = the chair
• bók = book → bók
  • in = bókin = the book
• kennari = teacher → kennari
  • nn = kennarinn = the teacher

Kennarinn is in the nominative singular, because it is the subject of the sentence – the one doing the action.

A very rough mini-paradigm for kennari (masculine noun):

• Nominative: kennari / kennarinn – teacher / the teacher
• Accusative: kennara / kennarann – (sees) the teacher
• Dative: kennara / kennaranum – (gives to) the teacher
• Genitive: kennara / kennarans – (of) the teacher

In Kennarinn notar nýja kennslubók í íslensku, the teacher is the one who uses, so nominative is required.

Nota is the infinitive: to use.
Notar is the 3rd person singular present tense: uses.

Present tense of að nota (to use):

• ég nota – I use
• þú notar – you (sg.) use
• hann / hún / það notar – he / she / it uses
• við notum – we use
• þið notið – you (pl.) use
• þeir / þær / þau nota – they use

Since the subject is kennarinn = the teacher (3rd person singular), we use notar.

Nýja is the accusative feminine singular form of the adjective nýr (new), agreeing with kennslubók, which is:

• feminine
• singular
• in the accusative (because it is the direct object: what is being used)

Pattern:

• Nominative fem. sg.: ný bók – a new book (subject)
• Accusative fem. sg.: nýja bók – (uses) a new book (object)

So:

• Kennarinn notar nýja kennslubók.
  
  • kennslubók = feminine accusative singular
  • the adjective must match: nýja

Change any of gender/case/number, and the adjective form changes too.

Kennslubók is a compound noun:

• kennsla = teaching, instruction
• bók = book

Together: kennslubók = textbook, teaching book.

Icelandic very often combines nouns into single compounds instead of writing them as separate words, similar to German:

• barn
  • skóli → barnaskóli – elementary school
• hand
  • bolti → handbolti – handball

So kennslubók is naturally written as one word, not kennsla bók.

In nýja kennslubók:

• Gender: Feminine
• Number: Singular
• Case: Accusative (direct object of notar)

Basic forms:

• Nominative: kennslubók – a textbook (subject)
• Accusative: kennslubók – (uses) a textbook
• Dative: kennslubók – (gives to) a textbook
• Genitive: kennslubókar – of a textbook

In the singular, nominative/accusative/dative look the same for this noun; you know it’s accusative from the function (object) and from the adjective form nýja.

Icelandic has no indefinite article (a / an).

• bók can mean a book or just book
• bókin means the book

So:

• ný kennslubók / nýja kennslubók = a new textbook
• nýja kennslubókin (with the article) = the new textbook

Indefiniteness (a/an) is simply absence of the definite article suffix.

Both í and á can be translated as in, but their use differs:

• á íslensku = in Icelandic as a language of communication

  • e.g. Hann talar á íslensku. – He speaks in Icelandic.

• í íslensku = in Icelandic as a school subject / area of study

  • e.g. kennslubók í íslensku – a textbook in the subject of Icelandic

So in this sentence, í íslensku describes the subject area of the textbook, which is why í is natural here.

Íslensku is in the dative singular, governed by the preposition í in this meaning.

The noun íslenska (the Icelandic language) – feminine:

• Nominative: íslenska
• Accusative: íslensku
• Dative: íslensku
• Genitive: íslensku

With í:

• í
  • dative is used for a static location or field/area (in the house, in math, in Icelandic [subject])
    
    • í húsinu – in the house
    • í stærðfræði – in mathematics
    • í íslensku – in Icelandic (as a school subject)

So íslensku here is dative singular feminine after í.

Yes, but the meaning or emphasis can change.

1. Kennarinn notar nýja kennslubók í íslensku.

   • Neutral: The teacher uses a new textbook in Icelandic (subject).

2. Kennarinn í íslensku notar nýja kennslubók.

   • Now í íslensku modifies kennarinn:
   • The Icelandic teacher (the teacher of Icelandic) uses a new textbook.
   • Similar to saying: Kennarinn í íslensku = the teacher in Icelandic (class).

3. Í íslensku notar kennarinn nýja kennslubók.

   • Fronts the phrase í íslensku for emphasis:
   • In Icelandic (class), the teacher uses a new textbook.

So the basic S–V–O order is stable, but moving í íslensku changes what it attaches to or what is emphasized.

In Icelandic, names of languages and nationalities are not capitalized, unless they appear at the beginning of a sentence.

• íslenska – Icelandic (language)
• dönsku – Danish
• ensku – English

Proper names like country names are capitalized:

• Ísland – Iceland
• Danmörk – Denmark
• Bretland – Britain

So íslensku in kennslubók í íslensku is correctly written with a lower-case initial letter.