Эта книга тонкая, но очень интересная.

Because книга is a feminine singular noun, and эта is the feminine singular form of этот (this).

Russian demonstratives must agree with the noun in:

• gender
• number
• case

So:

• этот = masculine
• эта = feminine
• это = neuter
• эти = plural

Since книга is feminine, you say эта книга = this book.

In Russian, many nouns ending in -а or -я are feminine, and книга follows that pattern.

So learners often recognize:

• книга → feminine
• машина → feminine
• неделя → feminine

Because книга is feminine, any adjectives or words like this that go with it must also be feminine:

• эта книга
• тонкая книга
• интересная книга

Because adjectives in Russian must agree with the noun they describe.

Here the noun is:

• книга = feminine singular, nominative

So the adjectives also take the feminine singular nominative ending:

• тонкий → тонкая
• интересный → интересная

A useful comparison:

• тонкий стол = a thin table / a narrow table (masculine)
• тонкая книга = a thin book (feminine)
• интересный фильм = an interesting film (masculine)
• интересная книга = an interesting book (feminine)

It is in the nominative case.

This sentence is a basic statement:

• Эта книга тонкая, но очень интересная.
• This book is thin, but very interesting.

The noun книга is the subject of the sentence, so it stays in the nominative case. The adjectives тонкая and интересная also appear in nominative because they describe the subject.

In the present tense, Russian usually leaves out the verb to be.

So instead of saying a literal version of This book is thin, Russian simply says:

• Эта книга тонкая.

That is completely normal Russian.

You do see forms of to be in other contexts, especially in the past and future:

• Книга была интересной. = The book was interesting.
• Книга будет интересной. = The book will be interesting.

But in the present tense, no separate word for is is needed.

Because но means but, and in Russian it normally joins two clauses or contrasting parts, just like English often does.

So:

• Эта книга тонкая, но очень интересная.

The comma marks the contrast:

• thin
• but very interesting

This is standard Russian punctuation.

Because очень means very, and in Russian it usually comes directly before the adjective or adverb it modifies.

So:

• очень интересная = very interesting

This is similar to English word order:

• very interesting
• очень интересная

You can think of очень as intensifying the adjective that follows it.

Because the sentence is making a statement about the book:

• This book is thin, but very interesting.

That structure is:

• noun phrase
  • description
• Эта книга
  • тонкая, но очень интересная

If you say эта тонкая книга, that means this thin book as one noun phrase. It sounds like you are identifying the book, not yet making a complete statement.

Compare:

• Эта книга тонкая. = This book is thin.
• Эта тонкая книга... = This thin book...

So in your sentence, тонкая and интересная are predicate adjectives describing the subject.

The dictionary forms are the masculine singular nominative forms:

• тонкий = thin
• интересный = interesting

Russian dictionaries usually list adjectives in that form. Then you change the ending to match the noun.

For книга (feminine singular), they become:

• тонкий → тонкая
• интересный → интересная

So when learning vocabulary, it is helpful to memorize:

• тонкий
• интересный

and then practice changing them for gender and number.

Yes. Тонкая книга naturally means a thin book, usually referring to a book with few pages or a small thickness.

So this sentence contrasts two ideas:

• the book is thin
• but it is very interesting

That contrast is exactly what но expresses.

Тонкая is pronounced approximately like TON-kaya, with the stress on the first syllable: то́нкая.

What is happening:

• тонк- is the stem
• -ая is the feminine ending

When spoken, the combination can sound a bit like -kaya:

• тонкая → TON-kaya

This is normal in Russian pronunciation. Many feminine adjective forms sound similar:

• интересная
• русская
• новая

For a learner, it is often easiest first to recognize the spelling pattern and then get used to the natural pronunciation through listening.