Learn Hardcore Icelandic: Kennslubókin útskýrir þessa reglu með mörgum góðum dæmum. - The textbook explains this rule with many good examples.

kennsla = teaching, instruction
→ kennslu- is the genitive/combining form used in compounds
bók = book
-in = the (definite article, feminine singular)

So:

kennslu + bók → kennslubók = textbook (literally teaching-book)
kennslubók + in → kennslubókin = the textbook

Icelandic usually forms things like textbook as a single compound rather than two separate words like kennslu bók.

Why is kennslubókin in this form and not something like kennslubók or kennslubókar?

Kennslubókin is:

nominative (subject case)
singular
feminine
definite (has -in, meaning the)

The verb útskýrir (explains) needs a subject in the nominative case. So we use the nominative definite form:

nominative indefinite: kennslubók = a textbook
nominative definite: kennslubókin = the textbook

Forms like kennslubókar would be other cases (e.g. genitive), which are not correct for the subject here.

Why is the verb útskýrir and not útskýra?

Útskýra is the infinitive form: to explain.
In the sentence we need the present tense, 3rd person singular, to match kennslubókin (the textbook):

Conjugation (present tense, singular):

ég útskýri = I explain
þú útskýrir = you (sg.) explain
hann / hún / það útskýrir = he / she / it explains

Kennslubókin is like hún (she; feminine singular), so we must use útskýrir:

Kennslubókin útskýrir … = The textbook explains …

Why is it þessa reglu and not þessi regla?

Because þessa reglu is in the accusative case, used for the direct object of the verb.

The verb útskýrir takes a direct object in the accusative:
- útskýrir hvað? → þessa reglu (explains what? this rule)

Forms:

regla (feminine noun = rule)
- nominative: regla (used as subject)
- accusative: reglu (used as direct object)
þessi (this) – feminine singular:
- nominative: þessi
- accusative: þessa

They have to agree:

nominative: þessi regla = this rule (as subject)
accusative: þessa reglu = this rule (as object)

Here the rule is the thing being explained, so we need accusative: þessa reglu.

What are the main forms of the noun regla (rule)?

Important singular and plural forms:

Singular:

nominative: regla (a rule – subject)
accusative: reglu (a rule – object)
dative: reglu
genitive: reglu

Plural:

nominative: reglur
accusative: reglur
dative: reglum
genitive: reglna or reglna/regla (you may see variation; reglna is common)

In the sentence, we need accusative singular, so we use reglu: þessa reglu.

Why does með mörgum góðum dæmum use the dative case?

The preposition með can take either accusative or dative, depending on the meaning.

When með means with, by means of, using, it takes the dative case.
Here it means: explains this rule *with / by means of many good examples* → dative.

So the whole phrase mörgum góðum dæmum is in dative plural:

dæmi (example), neuter:
- nom/acc plural: dæmi
- dative plural: dæmum

Adjectives and quantifiers have to agree in case, number, and gender:

margur (many), neuter dative plural: mörgum
góður (good), neuter dative plural: góðum
dæmi, neuter dative plural: dæmum

So we get: með mörgum góðum dæmum.

Why do all three words change in mörgum góðum dæmum? Why not just change dæmi?

In Icelandic, adjectives and quantifiers agree with the noun in:

case (here: dative)
number (here: plural)
gender (here: neuter)

So:

dæmi is neuter, plural, dative → dæmum
margur must match: neuter, plural, dative → mörgum
góður must match: neuter, plural, dative → góðum

You cannot leave mörg góð dæmi (that would be nominative/accusative); the preposition með forces everything in the phrase to dative: mörgum góðum dæmum.

Could I say með mörg góð dæmi instead of með mörgum góðum dæmum?

No, not in this sentence.

með here requires the dative case, so the correct forms are:
- mörgum (dative plural)
- góðum (dative plural)
- dæmum (dative plural)

Mörg góð dæmi would be nominative or accusative plural, which would clash with með in this meaning. So:

✔ með mörgum góðum dæmum
✘ með mörg góð dæmi (wrong case here)

Why is there no separate word for the in kennslubókin, but there is þessa before reglu?

Icelandic usually shows definiteness by adding an article ending to the noun, rather than a separate word:

bók = book
bókin = the book

With the compound:

kennslubók = textbook
kennslubókin = the textbook

For þessa reglu, we are using þessi (this) as a demonstrative, not just a plain definite article. So:

reglan = the rule (definite article ending)
þessi regla / þessa reglu = this rule (demonstrative, declined for case)

In the sentence, the speaker wants to point to a specific rule, so þessa reglu (this rule) is more precise than just regluna (the rule).

Is the word order Kennslubókin útskýrir þessa reglu með mörgum góðum dæmum fixed, or can it be changed?

This is the most natural, neutral word order:

Subject: Kennslubókin
Verb: útskýrir
Object: þessa reglu
Adverbial phrase: með mörgum góðum dæmum

Icelandic allows some flexibility, especially for emphasis, but you must keep the verb in second position in main clauses.

Examples (all grammatical, but with different emphasis):

Kennslubókin útskýrir þessa reglu með mörgum góðum dæmum.
– neutral, most common.
Kennslubókin útskýrir með mörgum góðum dæmum þessa reglu.
– extra emphasis towards þessa reglu at the end.

Starting with the adverbial is also possible, but then the verb still has to be second:

Með mörgum góðum dæmum útskýrir kennslubókin þessa reglu.
– emphasises with many good examples.

All of these are acceptable; they just sound slightly different in focus.

How would this sentence change if examples were singular instead of plural?

If we wanted with a good example (singular), we would make the whole phrase singular, still in the dative:

dæmi (example), neuter singular:
- nom/acc: dæmi
- dative: dæmi (same form)
margur (many) would no longer be used; we might use einum (one) or just drop the number.
góður (good), neuter dative singular: góðu

Examples:

með einu góðu dæmi = with one good example
með góðu dæmi = with a good example

So the full sentence could be:

Kennslubókin útskýrir þessa reglu með einu góðu dæmi.
Kennslubókin útskýrir þessa reglu með góðu dæmi.

How is dæmum formed from dæmi?

Dæmi (example) is a neuter noun with a regular plural pattern:

Singular:
- nom/acc: dæmi
- dat: dæmi
- gen: dæmis
Plural:
- nom/acc: dæmi
- dat: dæmum
- gen: dæma

So dæmum is the dative plural form, used here because of með:

með dæmum = with examples (in the sense: by means of examples)
→ then we add mörgum and góðum to make með mörgum góðum dæmum.