Не мог бы ты одолжить мне свою книгу до завтра?

Because Не мог бы ты... ? is a standard polite way to make a request in Russian.

Literally, it is close to Couldn’t you...? or Wouldn’t you be able to...? In both Russian and English, this kind of negative wording can sound softer and less direct than a plain command.

Compare:

• Одолжи мне книгу. — Lend me the book. (direct)
• Можешь одолжить мне книгу? — Can you lend me the book? (neutral)
• Не мог бы ты одолжить мне книгу? — Could you lend me the book? (more polite / softer)

So the не does not make the whole meaning negative in practice; it softens the request.

On its own, yes, мог is the past tense of мочь (to be able to). But in Russian, the combination past tense + бы is a common way to express the conditional mood.

So:

• мог = could / was able
• мог бы = could / would be able to

That is why Не мог бы ты... ? means Could you...? rather than something strictly about the past.

This is one of the most common polite request patterns in Russian.

бы is a particle that helps form the conditional meaning.

Without бы, the sentence would sound more like a straightforward statement or question about ability:

• Ты не мог одолжить мне книгу? — this sounds like asking whether you were unable / weren’t able to lend it, which is not the intended polite request.

With бы:

• Не мог бы ты одолжить мне книгу? — Could you lend me the book?

So бы is essential here. It turns мог into the kind of tentative, polite could / would meaning that English speakers expect in requests.

Yes. ты is informal singular, used with friends, family, children, or people you know well.

So this sentence is informal:

• Не мог бы ты одолжить мне свою книгу до завтра?

If you want to be polite, formal, or if you are speaking to more than one person, you would use Вы:

• Не могли бы Вы одолжить мне свою книгу до завтра?

Notice that the verb also changes:

• ты → мог бы
• Вы → могли бы

So the sentence as given sounds like the speaker is talking to one person informally.

This is about aspect.

• одолжить = perfective
• одалживать = imperfective

In this sentence, the speaker is asking for one complete action: to lend the book for this occasion. That is why the perfective одолжить is natural.

So:

• Не мог бы ты одолжить мне свою книгу до завтра?
  = Could you lend me your book until tomorrow?

If you used the imperfective, it would sound less natural here unless you meant repeated action, process, or a more general habit.

In polite requests for a single result, Russian very often prefers the perfective infinitive.

This is a very common source of confusion.

In this sentence, одолжить мне книгу clearly means lend me a book.

Why? Because the structure is:

• одолжить
  • thing in the accusative + person in the dative

Here:

• книгу = the thing being lent
• мне = to me

So the meaning is lend me your book.

In standard Russian:

• одолжить кому-то что-то = to lend someone something

For borrow, learners are often taught:

• взять взаймы
• sometimes занять in colloquial use, depending on region and speaker

So in this sentence, you should definitely understand одолжить as lend, not borrow.

мне is the dative case of я.

Russian uses the dative for the indirect object — the person who receives something.

Here:

• одолжить что? — книгу
• одолжить кому? — мне

So мне means to me.

That is why the sentence means:

• Could you lend me your book until tomorrow?

not

• Could you lend my book...

Because Russian usually uses свой to refer to something belonging to the subject of the clause.

Here the subject is ты, so свою книгу means your own book.

Breakdown:

• свой = reflexive possessive adjective, meaning roughly one’s own
• свою = the form of свой that agrees with книгу (feminine singular accusative)

So:

• Не мог бы ты одолжить мне свою книгу...?
  = Could you lend me your book...?

Russian strongly prefers свой in this kind of situation.

You can sometimes use твою for emphasis or contrast, for example if you want to stress your book, not someone else’s. But the neutral, standard choice here is свою.

Because книгу is in the accusative case, which is used here for the direct object of the verb.

The dictionary form is:

• книга = book

But after одолжить (to lend), the thing being lent is the direct object, so it goes into the accusative:

• одолжить что? — книгу

Since книга is a feminine noun ending in -а, its accusative singular changes to -у:

• книга → книгу

Literally, до завтра means until tomorrow / before tomorrow / up to tomorrow, depending on context.

In this sentence, the natural meaning is:

• Could you lend me your book until tomorrow?

That suggests the speaker wants to keep the book and return it tomorrow.

In general, до + time expression marks a limit:

• до вечера — until evening
• до понедельника — until Monday
• до завтра — until tomorrow

So here it tells you how long the speaker wants to have the book.

Yes. Russian word order is more flexible than English word order, and changing it often affects emphasis, not basic meaning.

For example, these are all possible:

• Не мог бы ты одолжить мне свою книгу до завтра?
• Не мог бы ты мне одолжить свою книгу до завтра?
• Не мог бы ты одолжить свою книгу мне до завтра?

The first one is very natural and neutral.

A few notes:

• putting мне earlier can slightly emphasize to me
• moving до завтра can emphasize the time limit
• not every possible order sounds equally natural, but Russian allows much more flexibility than English

So the exact order in the original sentence is normal and idiomatic, but it is not the only grammatically correct option.

There are several levels of directness:

• Одолжи мне свою книгу до завтра.
  Direct command: Lend me your book until tomorrow.

• Ты можешь одолжить мне свою книгу до завтра?
  Neutral question: Can you lend me your book until tomorrow?

• Не мог бы ты одолжить мне свою книгу до завтра?
  Softer, more polite: Could you lend me your book until tomorrow?

So the version in your sentence is not extremely formal, but it is definitely softer and more courteous than a plain command.