Bókin mín er á náttborðinu við hliðina á glasinu.

Because Icelandic usually puts the definite article at the end of the noun instead of using a separate word like English the.

• bók = book
• bókin = the book

So Bókin mín literally looks like book-the my, but it means my book.

That is a very common Icelandic pattern.

• bókin mín = my book
• literally: the-book my

In Icelandic, possessives often come after the noun, especially in ordinary, neutral speech. If the possessive comes after the noun, the noun is usually definite:

• bókin mín = my book

You can also put the possessive first:

• mín bók

But that often sounds more emphatic or contrastive, and then you normally do not add the definite ending to the noun.

Because mín has to agree with bókin in gender, number, and case.

The noun bók is:

• feminine
• singular
• here nominative

So the possessive must match:

• masculine: minn
• feminine: mín
• neuter: mitt

Since bókin is feminine singular nominative, mín is the correct form.

It is in the nominative case because it is the subject of the sentence.

The sentence structure is:

• Bókin mín = subject
• er = verb
• the rest = location

So Icelandic uses nominative here just as English uses the subject form in My book is...

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

Since the subject is singular:

• Bókin mín er ... = My book is ...

Compare:

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

Both words are:

• neuter
• singular
• definite
• in the dative case

Their dictionary forms are:

• náttborð = nightstand / bedside table
• glas = glass

In this sentence they appear as:

• náttborðinu = on the nightstand
• glasinu = next to the glass

The ending -inu is a typical dative singular definite ending for many neuter nouns.

Because of the prepositions used with a location meaning.

The first preposition is á. With á, Icelandic often distinguishes:

• accusative for movement onto something
• dative for location on something

So:

• Bókin er á náttborðinu = the book is on the nightstand → dative
• Ég set bókina á náttborðið = I put the book onto the nightstand → accusative

Similarly, in við hliðina á glasinu, the noun after á is also in the dative.

They do two different jobs.

1. á náttborðinu
   Here á means on.

2. við hliðina á glasinu
   Here the second á is part of the fixed expression við hliðina á, which means next to / beside.

So even though the same word appears twice, the two parts are functioning differently.

It is a very common Icelandic expression meaning next to or beside.

Learners often do best to memorize it as a whole chunk:

• við hliðina á = next to / beside

Word-for-word, it is something like by the side of, which helps explain why there is an extra á before glasinu.

Examples:

• við hliðina á húsinu = next to the house
• við hliðina á mér = next to me

Yes. Icelandic makes compound nouns very freely.

• nátt = night
• borð = table

So náttborð is literally night-table, i.e. nightstand / bedside table.

Then Icelandic adds endings to that whole compound:

• náttborð = nightstand
• náttborðið = the nightstand
• náttborðinu = on/to the nightstand, depending on context

Yes, to some extent. Icelandic word order is a bit more flexible than English, especially with adverbial phrases like places and directions.

The version here is a very natural, neutral one:

• Bókin mín er á náttborðinu við hliðina á glasinu.

It first tells you the main location (on the nightstand) and then adds a more specific detail (next to the glass).

You may see other orders in real Icelandic, but this version is clear and idiomatic.

A useful way to break it down is:

• Bókin mín = subject
• er = verb
• á náttborðinu = first location phrase
• við hliðina á glasinu = extra phrase giving more exact position

So the sentence builds the location in two steps:

1. the book is on the nightstand
2. more specifically, it is next to the glass

That layered structure is very common in Icelandic.