Какую бы книгу я ни читал, я всё равно записываю новые слова в тетрадь.

It is a very common Russian pattern meaning no matter which book I read / whatever book I am reading.

The structure is:

question word + бы + ... + ни + verb

Here:

• какую = which / what kind of
• бы ... ни together create the idea of no matter ... / whatever ...

So this is not a literal question. It is a concessive pattern: the specific book does not matter.

You will see the same pattern with other words too:

• Кто бы ни пришёл... = Whoever comes...
• Где бы он ни жил... = Wherever he lives...
• Что бы ты ни сказал... = Whatever you say...

Because книга is the object of читать, so it must be in the accusative case.

• dictionary form: книга
• accusative singular: книгу

The word какую is the accusative feminine singular form of какой, and it agrees with книгу in:

• gender: feminine
• number: singular
• case: accusative

So:

• какая книга = which book (nominative)
• какую книгу = which book as a direct object

In this construction, бы and ни work together to create the meaning no matter which / whatever.

Important point:

• бы here is not simply the English would
• ни here is not ordinary negation like not

Together, they form a set expression pattern.

Compare:

• Какую книгу ты читаешь? = Which book are you reading?
• Какую бы книгу я ни читал... = Whatever book I read... / No matter which book I read...

So the pair бы ... ни is a signal that the clause is not asking a question, but expressing free choice / irrelevance of the choice.

This is one of those places where Russian grammar does not match English very closely.

After бы, Russian commonly uses the past-tense form of the verb, but the meaning is not necessarily past. In this pattern, читал does not mean I was reading in past time. It is part of the construction meaning whatever I read / may read / happen to be reading.

Also, читал agrees with the speaker’s gender:

• я читал = said by a man
• я читала = said by a woman

So if the speaker were female, the sentence would be: Какую бы книгу я ни читала, я всё равно записываю новые слова в тетрадь.

Because the main clause describes a regular, repeated habit.

• записываю = imperfective present, meaning I write down / I keep writing down
• запишу = perfective future, meaning I will write down once or as a completed act
• записал = past, I wrote down

Here the idea is habitual: Whenever I read any book, I still write down new words.

That is exactly the kind of meaning Russian often expresses with the imperfective present.

Всё равно means something like:

• all the same
• anyway
• regardless
• still

It emphasizes that the action in the main clause happens regardless of the book.

So:

• Какую бы книгу я ни читал, я записываю новые слова... = Whatever book I read, I write down new words...
• Какую бы книгу я ни читал, я всё равно записываю новые слова... = Whatever book I read, I still / anyway write down new words...

Without всё равно, the sentence is still correct. With it, the sense of regardless of circumstances is stronger.

Because Russian often uses:

• в + accusative for direction / into
• в + prepositional for location / in

Here:

• в тетрадь = into the notebook
• в тетради = in the notebook

With записывать, Russian often imagines the words as being entered into the notebook, so в тетрадь is very natural.

Compare:

• Я пишу в тетради. = I am writing in a notebook.
• Я записываю слова в тетрадь. = I write words down into a notebook.

So the accusative here fits the idea of putting information into the notebook.

Not completely, but this order is the most natural and standard.

A useful rule is:

• бы usually comes right after the question word or the phrase built from it
• ни usually comes before the verb

So:

• Какую бы книгу я ни читал sounds normal and idiomatic.

Russian word order is flexible, but not every rearrangement sounds equally natural. For learners, it is best to remember this pattern as a chunk:

какую бы книгу я ни читал

That will help you produce similar sentences correctly:

• Какой бы фильм мы ни смотрели...
• Сколько бы времени у меня ни было...
• Куда бы он ни пошёл...

No. That is a very important distinction.

• не is the basic negation word: not
• ни often appears in special constructions like this one, where it helps create meanings such as no matter..., whoever..., wherever...

In this sentence, ни does not simply negate the verb.
You should not read я ни читал as I did not read.

Instead, the whole pattern какую бы ... ни читал means: whatever ... I read

So here ни is part of the idiomatic grammatical structure, not ordinary sentence negation.