Learn Icelandic: Hún á bláa bók.

In Icelandic, adjectives must match the noun they describe in gender, number, and case. The word bók is a feminine noun in the accusative case here. For strong adjectives, the feminine accusative singular ending is -a. Therefore, the dictionary form blár becomes bláa.

Why use á for "has" instead of hefur?

The verb eiga (which becomes á for "she has") is used for direct ownership. Since she owns the physical book, we use á. The other word for "to have" is hafa (hefur), but that is mostly used as a helping verb or for abstract things you cannot physically own.

What puts the book in the accusative case in the first place?

The book is the direct object of the sentence because it is the thing being owned. In Icelandic, the verb eiga requires its direct object to be in the accusative case.

If the book is in the accusative case, why doesn't the word bók change its spelling?

Not all nouns change their spelling in every case. For many feminine nouns like bók, the accusative form is exactly the same as the basic dictionary form. Even though the noun doesn't change visibly, the adjective bláa proves that the phrase is in the accusative case!