الكتاب على السطح.

Because Arabic often uses nominal sentences in the present tense without a verb like is/are.

So:

• الكتاب = the book
• على السطح = on the roof / on the surface

Together, الكتاب على السطح naturally means The book is on the roof.

If you wanted a past-tense meaning, Arabic would usually add a verb such as كان.

This is a nominal sentence (جملة اسمية).

It has two main parts:

• الكتاب = the subject/topic (مبتدأ)
• على السطح = the predicate/comment (خبر)

The second part tells us something about the first part: where the book is.

Because ال is the Arabic definite article, meaning the.

So:

• كتاب = a book / book
• الكتاب = the book
• سطح = a roof / surface
• السطح = the roof / the surface

In this sentence, both nouns are definite: the book and the roof.

In careful pronunciation, the ل of ال changes in sound here because س is a sun letter.

So السطح is pronounced more like:

• as-saṭḥ

not fully al-saṭḥ in normal pronunciation.

This happens because the l sound of ال assimilates to the following sun letter.

By contrast, in الكتاب, ك is a moon letter, so you do pronounce the l:

• al-kitāb

على usually means on, on top of, or sometimes upon.

In this sentence, it expresses location:

• على السطح = on the roof / on the surface

It is a preposition.

Yes. على is a preposition, and in Arabic, a noun after a preposition is put in the genitive case (مجرور).

In fully vowelled Arabic, the sentence would be:

• الكتابُ على السطحِ

Notice:

• الكتابُ ends in -u because it is the subject of the nominal sentence
• السطحِ ends in -i because it comes after the preposition على

In everyday writing, these short vowel endings are usually not written.

In normal Arabic writing, short case endings are usually omitted.

So you usually see:

• الكتاب على السطح

But in a fully vocalized form, it would be:

• الكتابُ على السطحِ

Those final vowels are part of the grammar, but they are often left unwritten except in the Qur’an, children’s books, textbooks, or very careful educational texts.

Yes, depending on context.

سطح can mean:

• roof
• surface
• sometimes top

So على السطح may mean on the roof or on the surface. Context tells you which meaning is intended.

This is the normal and simple order for a nominal sentence:

• subject/topic first
• then the information about it

So:

• الكتاب على السطح = The book is on the roof

You can change the order for emphasis, for example:

• على السطح الكتاب

But that is less neutral and more marked. For a beginner, الكتاب على السطح is the standard pattern to learn.

Yes, but the meaning shifts slightly.

• على السطح usually suggests on the surface / on top of, often with contact
• فوق السطح means above the roof / over the roof / on top of the roof, and can sometimes focus more on position above

In many contexts they may be close, but على is the most direct translation of on.

Yes. It is a prepositional phrase:

• على = preposition
• السطح = noun governed by that preposition

Together, على السطح functions as the predicate of the sentence and tells you the location of the book.

A common transliteration is:

• al-kitābu ʿalā as-saṭḥi

If you ignore case endings, you might also see:

• al-kitāb ʿalā as-saṭḥ

A few notes:

• ā represents a long a
• ʿ represents the letter ع
• ṭ represents an emphatic t
• the s in as-saṭḥ shows the assimilation of ال before a sun letter

Yes, but the wording would change.

For A book is on the roof, you could say:

• كتابٌ على السطحِ

However, Arabic often prefers definite topics in simple nominal sentences, so context matters. Beginners will very often first meet the definite pattern:

• الكتاب على السطح

which is straightforward and very common.