Я купил клей и бумагу, чтобы сделать новую обложку для тетради.

Купил is the perfective past form of купить, so it presents the action as completed: the speaker bought the glue and paper.

Compare:

• Я купил клей и бумагу = I bought the glue and paper.
• Я покупал клей и бумагу = I was buying / used to buy glue and paper / bought them at some point, with less focus on the completed result.

In this sentence, the completed result matters, because the speaker bought the materials in order to make something.

In Russian, the past tense is often built from the verb stem plus -л. The ending also shows gender and number.

Here:

• купил = masculine singular past
• купила = feminine singular past
• купило = neuter singular past
• купили = plural

So Я купил tells us the speaker is male. If the speaker were female, it would be:

• Я купила клей и бумагу...

Because бумага is the direct object of купил, it goes into the accusative case.

• Nominative: бумага
• Accusative: бумагу

So:

• Я купил бумагу = I bought paper

This is very common with feminine nouns ending in -а:

• книга → книгу
• тетрадь does not follow this pattern because it has a different ending and declension type.

Клей is also a direct object, so it is also in the accusative case. But for many inanimate masculine nouns, the accusative singular is the same as the nominative singular.

So:

• Nominative: клей
• Accusative: клей

That is why you see:

• Я купил клей
• not a visibly different form

This is normal in Russian. Some nouns show a visible change in the accusative, and some do not.

Чтобы here means in order to / so that. It introduces a purpose.

So:

• Я купил клей и бумагу, чтобы сделать новую обложку... = I bought glue and paper in order to make a new cover...

It explains why the speaker bought those things.

A very useful pattern is:

• [main action], чтобы + infinitive
• Я пришёл, чтобы помочь. = I came to help.
• Она позвонила, чтобы спросить. = She called to ask.

When the subject is the same in both parts of the sentence, Russian often uses:

• чтобы + infinitive

Here, the same person both bought the materials and wants to make the cover:

• Я купил... чтобы сделать...

If Russian wants to express a different subject more explicitly, it often uses a finite verb after чтобы:

• Я купил клей и бумагу, чтобы она сделала обложку. = I bought glue and paper so that she would make the cover.

So the infinitive works naturally here because the doer is the same person.

Сделать is the perfective verb, while делать is imperfective.

• делать = to do/make, process, ongoing action
• сделать = to make/do, with emphasis on completion/result

Here the goal is to produce a finished cover, so сделать is the natural choice.

Compare:

• чтобы сделать новую обложку = in order to make a new cover, with a finished result
• чтобы делать обложки = in order to make covers, perhaps regularly or as an activity

Because обложка is the direct object of сделать, it must be in the accusative case, and the adjective must agree with it.

Forms:

• Nominative: новая обложка
• Accusative: новую обложку

Both words change:

• новая → новую
• обложка → обложку

This is standard adjective-noun agreement in Russian: the adjective matches the noun in gender, number, and case.

After для meaning for, Russian uses the genitive case.

So:

• Nominative: тетрадь
• Genitive: тетради

That is why the sentence says:

• обложку для тетради = a cover for a notebook

This is a very common pattern:

• подарок для друга = a gift for a friend
• чашка для чая = a cup for tea
• обложка для тетради = a cover for a notebook

Russian often expresses this idea with для + genitive when the meaning is a cover intended for a notebook.

• обложка для тетради = a cover for a notebook

This sounds natural when talking about the function or purpose of the object.

A possessive-style idea is possible in some contexts, but it may sound different in meaning or style. Here, для тетради is the most straightforward and natural way to say that the cover is for the notebook.

Russian word order is more flexible than English word order, because case endings do a lot of the grammatical work.

The given sentence is neutral and natural:

• Я купил клей и бумагу, чтобы сделать новую обложку для тетради.

But other orders are possible for emphasis, for example:

• Клей и бумагу я купил, чтобы сделать новую обложку для тетради.
  This emphasizes what was bought.

• Чтобы сделать новую обложку для тетради, я купил клей и бумагу.
  This emphasizes the purpose first.

So the original order is normal, but not the only possible one.

In this sentence, бумагу most naturally means paper as a material, not necessarily one single sheet.

So:

• Я купил клей и бумагу... = I bought glue and paper...

If you wanted to be more specific about a sheet / sheets of paper, Russian would often say something like:

• лист бумаги = a sheet of paper
• листы бумаги = sheets of paper

But in your sentence, бумагу is a natural general word for paper.

Тетрадь means notebook or exercise book, usually a thin book of blank or lined pages used for writing.

Книга means book.

So:

• обложка для тетради = a cover for a notebook
• обложка для книги = a cover for a book

A learner might expect notebook to be something like a modern bound notebook, and тетрадь can indeed mean that, but it often especially refers to the kind of notebook used in school.

Yes, often it can.

Russian does not always need the subject pronoun when it is clear from the verb form or the context. So this is also possible:

• Купил клей и бумагу, чтобы сделать новую обложку для тетради.

However, я is perfectly natural if you want to be explicit, add contrast, or simply sound slightly clearer.

In beginner examples, Russian often includes я more often than native speech does, because it helps learners see who is doing the action.