Bókin er fallegri en ég hélt.

Because Icelandic usually puts the definite article at the end of the noun.

• bók = book
• bókin = the book

So bókin is the definite form: the book.

Bókin is feminine singular nominative.

• bók is a feminine noun
• the sentence subject is the book
• subjects of er are normally in the nominative

So bókin is the nominative singular definite form.

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

So:

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

Here, bókin er means the book is.

Fallegri is the comparative of fallegur = beautiful.

So:

• fallegur / falleg / fallegt = beautiful
• fallegri = more beautiful / prettier

Icelandic often makes comparatives with an adjective ending, instead of using a separate word like English more.

Because adjectives in Icelandic still agree with the noun in gender, number, and case, even in the comparative.

Here the subject is bókin, which is feminine singular nominative, so the adjective appears as fallegri.

For comparison:

• Bókin er fallegri. = The book is prettier.
• Húsið er fallegra. = The house is prettier.

Here húsið is neuter, so the comparative form changes.

Here en means than.

After a comparative adjective, en introduces the comparison:

• fallegri en... = more beautiful than...

Be careful: en can also mean but in other sentences. In this sentence, because it follows a comparative, it clearly means than.

The verb halda has several meanings. One common meaning is to think, to suppose, or to believe in certain contexts.

So ég hélt means I thought or I assumed.

This past tense form is irregular:

• halda = to think / suppose
• hélt = thought

So this is something you mostly have to learn as a set expression.

Because the sentence is using ellipsis: words are left out because they are easy to understand from context.

A fuller version could be:

Bókin er fallegri en ég hélt að hún væri.
= The book is more beautiful than I thought it was.

But Icelandic, like English, often leaves that last part unstated when it is obvious.

Yes. Fallegri is just the Icelandic comparative form. In English, you might translate it as either:

• prettier
• more beautiful

Both are natural, and the best choice depends on style and context rather than on a difference in the Icelandic word itself.