Þessi bók er svipuð bókinni sem þú lest.

Because bók is a feminine singular noun, and the demonstrative þessi has to agree with it in gender, number, and case.

• þessi = feminine singular nominative
• þetta = neuter singular nominative

So þessi bók means this book.

The adjective has to agree with the subject, þessi bók, which is feminine singular nominative.

So the adjective appears in the matching form:

• masculine: svipaður
• feminine: svipuð
• neuter: svipað

Because bók is feminine, Icelandic uses svipuð.

Because the adjective svipaður / svipuð / svipað normally takes the thing it is compared to in the dative case.

So:

• bókin = the book in nominative
• bókinni = the book in dative

In this sentence, svipuð means similar to, and Icelandic expresses that to idea through the dative case rather than with a separate preposition.

It is the noun bók with the definite article and dative singular ending.

A simplified breakdown is:

• bók = book
• bókin = the book
• bókinni = to/the book, the book in dative

For feminine nouns like bók, the dative singular definite form often ends in -inni.

Sem introduces a relative clause, like that, which, or that ... who/which in English.

So:

• bókinni sem þú lest = the book that you are reading / the book you read

It links bókinni to the clause þú lest and tells us which book is meant.

Because sem already does that job. Icelandic relative clauses are often very compact.

So:

• bókinni sem þú lest literally works like the-book-DAT that you read

English sometimes needs more structure, but Icelandic can express it very directly with sem.

Lest is the present tense of the verb lesa (to read), for þú (you, singular).

So:

• ég les = I read / I am reading
• þú lest = you read / you are reading

As often happens in Icelandic, the present tense can correspond to either simple present or present progressive in English, depending on context.

Because it is part of the relative clause introduced by sem:

• sem þú lest = that you are reading

This is normal Icelandic word order for a relative clause: relative word + subject + verb.

So the full structure is:

• Þessi bók = subject
• er svipuð = is similar
• bókinni sem þú lest = to the book that you are reading

Yes, structurally that is possible, but it would usually sound odd unless you meant something very specific. In your sentence, bókinni sem þú lest identifies a different book: the book that you are reading.

The important grammar point is that after svipuð, the compared noun phrase goes into the dative:

• svipuð bókinni
• svipuð þessari bók

It describes bókinni.

So the meaning is:

• This book is similar to [the book that you are reading].

It does not mean:

• This book, which you are reading, is similar ...

If Icelandic wanted the relative clause to describe þessi bók, the structure would be different.

Because many Icelandic adjectives govern a particular case directly. In this case, svipaður / svipuð / svipað takes the dative.

English uses a preposition:

• similar to the book

Icelandic often does the same idea with case alone:

• svipuð bókinni

This is something English speakers often need to get used to: Icelandic case endings often express relationships that English shows with prepositions.

The dictionary forms are:

• þessi = this
• bók = book
• vera = to be
• svipaður = similar
• bók = book
• sem = that / which
• þú = you
• lesa = to read

In the sentence, some of these appear in inflected forms:

• svipuð from svipaður
• bókinni from bók
• lest from lesa
• er from vera