ده نفس الكتاب.

ده is the Egyptian Arabic masculine singular demonstrative. It usually means this or that.

At the start of this sentence, ده works like this is or that is. So ده نفس الكتاب means This/That is the same book.

Because كتاب is masculine singular, ده is the right form here.

In Arabic, the present-tense verb to be is usually omitted.

So where English says This is the same book, Egyptian Arabic just says:

ده نفس الكتاب

Literally, it is closer to this same the-book.

Because ده is being used as a standalone demonstrative pronoun here.

There is an important difference:

الكتاب ده = this book
This is a noun phrase.

ده نفس الكتاب = this/that is the same book
This is a full sentence.

So when ده comes first, it is not modifying الكتاب directly. It is the subject of the sentence.

Here, نفس means same.

So:

نفس الكتاب = the same book

But نفس is a very flexible word. In other contexts, it can also mean things like self or soul, depending on the construction.

For this sentence, the important meaning is simply same.

Because when نفس means same, the noun after it is usually definite or otherwise specific.

So:

نفس الكتاب = the same book
not a same book

You can also make it specific in other ways, not only with ال:

نفس فكرتي = the same idea as mine
نفس العربية = the same car

Because نفس الكتاب is built like an iḍāfa-type construction, where the first word normally does not take ال, and the definiteness comes from the second word.

So even though the whole phrase means the same book, only الكتاب takes ال:

نفس الكتاب

not النفس الكتاب

This is very normal Arabic structure.

A common Egyptian pronunciation is:

da nafs el-ketāb

A few useful notes:

ده is often written ده but pronounced da
نفس is nafs
الكتاب in Egyptian is commonly el-ketāb

So if you say da nafs el-ketāb, that will sound natural.

In everyday Egyptian Arabic, ده can often be translated as either this or that, depending on context.

So ده نفس الكتاب could be understood as:

This is the same book
or
That is the same book

Usually the situation, pointing, or tone of voice makes it clear.

They are close, but not exactly the same.

ده نفس الكتاب means This/That is the same book.
This is used when you are comparing it with another previously mentioned book.

ده الكتاب نفسه means This/That is the book itself or this very book.
This is more emphatic and focuses on the book itself.

So the safest distinction is:

نفس الكتاب = the same book
الكتاب نفسه = the book itself

The demonstrative would change.

Masculine singular:
ده نفس الكتاب = This is the same book

Feminine singular:
دي نفس المجلة = This is the same magazine

Plural:
دول نفس الكتب = These are the same books

So ده is specifically for masculine singular.

Yes, but then it is just a noun phrase, not a full sentence.

نفس الكتاب = the same book

That can work as a short answer or sentence fragment, but if you want the full meaning This is the same book, you need ده:

ده نفس الكتاب