Ég vil kaupa bókina sem er á borðinu.

Because bókina is the form needed for a direct object.

• bókin = the book in the nominative case, usually used for the subject
• bókina = the book in the accusative case, used here because it is the thing being bought

In this sentence, ég is the subject and bókina is the object of kaupa.

In Icelandic, the definite article is usually added to the end of the noun instead of being a separate word.

So:

• bók = book
• bókin = the book
• bókina = the book in the accusative

This is one of the first big differences English speakers notice, since English uses a separate word the.

The dictionary form is að kaupa = to buy, but after verbs like vilja (to want), Icelandic normally uses the infinitive without að.

So:

• að kaupa = to buy
• ég vil kaupa = I want to buy

This is similar to English, where we also say I want to buy, not I want to to buy.

Vil is the present-tense form of vilja, meaning to want.

So:

• ég vil = I want

It is followed by another verb in the infinitive, here kaupa.

Here sem is a relative particle/pronoun, meaning something like that, which, or sometimes who, depending on context.

In bókina sem er á borðinu, it introduces extra information about the book:

• bókina = the book
• sem er á borðinu = that is on the table

So sem links the noun to the relative clause that describes it.

No. One useful thing about sem is that it stays the same.

Unlike many other words in Icelandic, sem does not change to match:

• masculine / feminine / neuter
• singular / plural
• nominative / accusative / dative / genitive

So learners often find sem pleasantly simple.

Er is the present tense of vera (to be) and means is here.

• sem er á borðinu = that is on the table

In standard Icelandic, you normally keep er in a full relative clause like this. English sometimes allows a shorter form such as the book on the table, but this Icelandic sentence uses the full structure the book that is on the table.

Because Icelandic uses different cases after many prepositions depending on meaning.

With á:

• accusative often suggests movement onto something
• dative often suggests location on something

Here the book is already on the table, so this is location, not movement. That is why Icelandic uses the dative:

• á borðinu = on the table

If something were being placed onto the table, you would expect the accusative instead.

Borðinu is the dative singular definite form of the neuter noun borð (table).

A few relevant forms are:

• borð = table
• borðið = the table
• borðinu = to/on/from the table, depending on the preposition and context

Since á here takes the dative for location, you get á borðinu.

The sentence follows a very common Icelandic pattern:

• Ég = subject
• vil = finite verb
• kaupa = infinitive
• bókina = object
• sem er á borðinu = relative clause describing the object

So the structure is basically:

Subject + finite verb + infinitive + object + description of the object

That is quite close to English word order in this sentence.

Sometimes you might hear a shorter noun phrase like that, but Ég vil kaupa bókina sem er á borðinu is clearer and safer for learners.

The version with sem er makes it explicit that the book is the thing located on the table. Without sem er, the phrase can feel more compressed and may depend more on context.

So if your goal is clear, standard Icelandic, the full relative clause is a very good choice.

The accent marks are part of the spelling and pronunciation. They are not optional.

For example:

• é
• ó
• á

are treated as distinct vowels in Icelandic, not just the plain vowels with decoration added. For learners, it is best to think of them as separate letters/sounds that must be learned as part of each word.

So you should write Ég and bókina, not Eg and bokina.