Málfræðin er ekki auðveld í þessum kafla.

The ending -in is the definite article attached to the noun. So:

• málfræði = grammar
• málfræðin = the grammar

Icelandic usually puts the at the end of the noun instead of using a separate word the way English does.

Because málfræði is a feminine singular noun, the definite form here is málfræðin.

Yes, málfræði is a feminine noun.

You often have to learn noun gender along with the word itself, but there are some common patterns. Many nouns ending in -i are masculine, but málfræði is one of many nouns in -fræði that are feminine.

This matters because other words in the sentence have to agree with it, especially the adjective:

• málfræðin = feminine singular
• auðveld = feminine singular form of easy

Because Icelandic adjectives must agree with the noun they describe.

Here, auðveld is describing málfræðin, which is feminine singular, so the adjective also has to be feminine singular.

Compare:

• auðveldur = masculine singular
• auðveld = feminine singular
• auðvelt = neuter singular

So:

• málfræðin er ekki auðveld = the grammar is not easy

If the noun were neuter, then auðvelt would be correct.

Because auðveld is being used predicatively, not directly before the noun.

Compare:

• auðveld málfræði = easy grammar
• málfræðin er auðveld = the grammar is easy

In the sentence you gave, the structure is:

• málfræðin = subject
• er = is
• auðveld = predicate adjective

Predicate adjectives agree with the subject in gender and number, but they are not marked for definiteness the way an attributive adjective can be.

In a normal Icelandic main clause, ekki usually comes after the finite verb.

So:

• Málfræðin er ekki auðveld.

That word order is completely normal and natural.

English also often puts not after a form of to be:

• is not

So this part is actually quite similar to English.

Er is the 3rd person singular present tense of the verb vera (to be).

So here it means is.

A few common forms of vera are:

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

Since málfræðin is singular, er is the correct form.

Because the preposition í takes the dative when it means in a place or location.

Here the meaning is in this chapter, so Icelandic uses the dative:

• í þessum kafla

Both words change form:

• þessi → þessum (dative singular masculine)
• kafli → kafla (dative singular)

So the phrase is in the dative because it describes location, not motion.

Þessum is the dative singular masculine form of the demonstrative þessi (this).

Since kafli is a masculine singular noun, and í requires the dative here, the correct form is:

• þessum kafla = this chapter (in the dative)

Very roughly:

• nominative: þessi kafli = this chapter
• dative after í: í þessum kafla = in this chapter

Because kafli is one of those masculine nouns whose nominative singular ends in -i, but other singular cases often use -a.

So:

• nominative: kafli
• accusative: kafla
• dative: kafla
• genitive: kafla

In your sentence, í requires the dative, so you get:

• í þessum kafla

This is very common in Icelandic masculine nouns of this type.

Yes, but the meaning changes a little.

• Málfræðin er ekki auðveld í þessum kafla.
  = The grammar is not easy in this chapter.
• Málfræði er ekki auðveld í þessum kafla.
  = Grammar is not easy in this chapter.

Without -in, the noun is more general or indefinite. With -in, it sounds more like a specific grammar section, grammar topic, or the grammar being discussed in context.

Yes. You can also say:

• Í þessum kafla er málfræðin ekki auðveld.

That means the same thing: In this chapter, the grammar is not easy.

Icelandic often moves adverbials like í þessum kafla to the front for emphasis or style. When that happens, the finite verb still stays in the usual second position:

• Í þessum kafla
  • er
    • málfræðin
      • ekki auðveld

This is a very common Icelandic word-order pattern.