Learn Icelandic: Er þetta gömul bók?

In Icelandic, adjectives change to match the gender of the noun they describe. The word for "book", bók, is a feminine noun. Therefore, the adjective must take its feminine singular form, which is gömul.

Where do the vowels "ö" and "u" in gömul come from if the dictionary form is gamall?

This is caused by a very common vowel shift in Icelandic. When certain endings are added to a word, an "a" in the root often changes to an "ö". You will see this a lot, but for now, it is easiest to just memorize gömul as the feminine version of "old".

If bók is feminine, why do we use the neuter word þetta for "this"?

When you point to something to identify it (like asking "Is this an old book?"), Icelandic always uses the default neuter form þetta, regardless of the noun's true gender. You would only use the feminine þessi if you were saying "This book is old" (Þessi bók er gömul).

Why is there no word for "an" in this sentence?

Icelandic does not have an indefinite article (words like "a" or "an" in English). Because of this, the phrase gömul bók translates directly to "an old book".