Kennslubókin er mjög áhugaverð.

Kennslubókin is made of three parts:

• kennsla – teaching, instruction
• bók – book
• -in – the definite article suffix for feminine nouns in the nominative singular

So:

• kennslubók = a textbook (literally: teaching‑book)
• kennslubókin = the textbook

The whole sentence is therefore talking about a specific textbook.

Icelandic (like the other Scandinavian languages) usually attaches the definite article to the end of the noun instead of putting a separate word before it.

For feminine nouns in the nominative singular, the definite ending is -in.
So:

• bók = book
• bókin = the book
• kennslubók = textbook
• kennslubókin = the textbook

There is a separate article hinn / hin / hið in Icelandic, but it is used differently and much less frequently than English the.

No, Icelandic does not capitalize all nouns. Here:

• Kennslubókin is capitalized only because it is the first word of the sentence.

Otherwise, kennslubók would be written with a lowercase k.

Kennslubókin is:

• Gender: feminine (because bók is a feminine noun)
• Case: nominative (it is the subject of the sentence)
• Number: singular
• Definiteness: definite (because of the suffix -in)

You can tell from:

• The base noun bók is listed as a feminine noun in dictionaries.
• The definite article ending -in is the nominative singular definite ending for many feminine nouns.

er is the present tense form of the verb að vera (to be), third person singular:

• ég er – I am
• þú ert – you are
• hann / hún / það er – he / she / it is

In this sentence, er corresponds to English is. In other contexts, er can also be:

• A relative pronoun meaning who / which / that (a different word, same spelling)

  But here it is clearly the verb to be.

No. mjög is an adverb meaning very, and adverbs in Icelandic do not decline for gender, case, or number.

So you use mjög in front of adjectives or other adverbs without changing it:

• mjög áhugaverð – very interesting
• mjög góður – very good
• mjög fljótt – very quickly

Adjectives in Icelandic agree with the noun they describe in:

• gender
• case
• number
• sometimes definiteness

The base form you see in dictionaries is usually masculine nominative singular, e.g.:

• áhugaverður – interesting (masc. nom. sg.)

But here the subject is kennslubókin, which is feminine nominative singular, so the adjective must match:

• Masculine: áhugaverður
• Feminine: áhugaverð
• Neuter: áhugavert

So we get Kennslubókin er mjög áhugaverð.

In predicate position after er, Icelandic usually uses the indefinite form of the adjective, even when the noun is definite.

So:

• Kennslubókin er mjög áhugaverð.
  The textbook is very interesting.

You only see the definite adjective form (with an extra ending like -i, -a, -a in many patterns) when the adjective is used directly before the noun in an attributive way, like:

• hin mjög áhugaverða kennslubók – the very interesting textbook

In your sentence, the adjective follows er, so it stays in the simple (indefinite) feminine form áhugaverð.

Grammatically, you could say it, but the meaning changes:

• kennslubók – a textbook (indefinite)
• kennslubókin – the textbook (definite)

So:

• Kennslubók er mjög áhugaverð.
  A textbook is very interesting. / Some textbook is very interesting.

This sounds unnatural without more context. In most realistic situations you are talking about a particular book, so kennslubókin is the normal choice.

Yes, here the word order matches standard English S–V–C (Subject–Verb–Complement):

• Kennslubókin – subject (the textbook)
• er – verb (is)
• mjög áhugaverð – subject complement (very interesting)

So the structure is parallel to:

• The textbook – is – very interesting.

Icelandic word order is fairly flexible, but S–V–X (subject–verb–rest) is the neutral pattern in simple statements.

Approximate pronunciation in IPA: [ˈcʰɛn̥stlʏˌpoukɪn]

A simple English-friendly guide:

• Kenns- – a bit like KENST, with a clear k and n
• -lu- – like li in little, but rounded (between luh and ly)
• -bó- – like BOH (long o, as in boat, without the t)
• -kin – like kin in English

Stress is on the first syllable: KENN-slubó-kin (main stress on KENN, secondary stress on bó).

Approximate IPA: [ˈauːɣʏˌvaˌvɛrð] (pronunciations vary a bit).

Rough English-style guide:

• á – like ow in now (a long au sound)
• huga – HU like hoo, but shorter, GA like ga in gallon (but softer g)
• verð – roughly like verth, with ð similar to the th in this, but often quite soft

Spelled syllables: á-hu-ga-verð
Main stress is on á: Á-huga-verð.

Yes, mjög áhugaverð is the most straightforward, but you might also see:

• rosa áhugaverð / rosalega áhugaverð – colloquial: really / super interesting
• afar áhugaverð – very / extremely interesting (a bit more formal)
• mjög spennandi – very exciting (slightly different nuance, but often used similarly in speech)

However, mjög áhugaverð is the neutral, safe choice in most contexts.