Після уроку я кладу зошит у рюкзак.

Because після always requires the genitive case.

• Base form: урок = lesson, class
• Genitive singular: уроку

So:

• після уроку = after the lesson / after class

This is a very common pattern in Ukrainian:

• після обіду = after lunch
• після роботи = after work
• після школи = after school

They are doing different jobs in the sentence.

• уроку comes after the preposition після, which requires the genitive
• зошит is the direct object of the verb кладу, so it is in the accusative

But here is the important detail: for many inanimate masculine nouns, the accusative singular looks exactly like the nominative singular.

So:

• Nominative: зошит
• Accusative: зошит

It has not stayed unchanged because it has no case; it is actually accusative, but the form happens to be the same.

Because this sentence expresses movement into the backpack, not location inside the backpack.

With у / в:

• у рюкзак = into the backpack → usually accusative
• у рюкзаку = in the backpack → usually locative

Compare:

• Я кладу зошит у рюкзак. = I put the notebook into the backpack.
• Зошит у рюкзаку. = The notebook is in the backpack.

This movement-vs-location contrast is very important in Ukrainian.

Кладу is the 1st person singular present tense form of класти.

So:

• я кладу = I put / I am putting

Some other forms are:

• ти кладеш
• він / вона кладе
• ми кладемо
• ви кладете
• вони кладуть

This verb is imperfective, so in the present tense it can mean either:

• a habitual action: I put
• an action happening now: I am putting

The exact meaning depends on context.

Because кладу and покладу differ in aspect.

• кладу = imperfective
• покладу = perfective

In this sentence, кладу most naturally suggests a habitual/repeated action:

• Після уроку я кладу зошит у рюкзак.
• After class, I put my notebook in my backpack.

If you wanted a single completed future action, you would more likely use покладу:

• Після уроку я покладу зошит у рюкзак.
• After class, I will put the notebook in the backpack.

Yes, often it can.

Ukrainian verbs usually show the subject clearly, so я is not always necessary.

• Після уроку кладу зошит у рюкзак.

This still means After class, I put/am putting the notebook into the backpack.

Including я can make the subject more explicit or slightly more emphatic. In learner sentences, it is also often included just for clarity.

Both у and в can mean in / into in many contexts. The choice is often made for euphony—to make the sentence sound smoother.

Here, у рюкзак sounds natural after зошит.

In many cases, Ukrainian speakers choose between у and в to avoid awkward sound combinations. So this is often about pronunciation flow, not a difference in meaning.

Very often, both are possible:

• у рюкзак
• в рюкзак

but one may sound more natural in context.

It can mean either, depending on context.

The noun урок can mean:

• lesson
• class period

So після уроку may be translated as:

• after the lesson
• after class

If the broader context is school, after class is often the most natural English translation.

No, Ukrainian word order is fairly flexible.

The neutral order here is:

• Після уроку я кладу зошит у рюкзак.

But you could rearrange it for emphasis, for example:

• Я після уроку кладу зошит у рюкзак.
• Зошит я кладу у рюкзак після уроку.

These versions are still understandable, but they may sound more marked or emphasize different parts of the sentence.

For learners, the original version is a good natural model.

Ukrainian does not have articles like a or the, so it does not need separate words for them.

Also, possession is often left implicit when it is obvious from context.

So:

• зошит could mean a notebook, the notebook, or my notebook
• рюкзак could mean a backpack, the backpack, or my backpack

If needed, Ukrainian can make possession explicit:

• мій зошит = my notebook
• мій рюкзак = my backpack

But in a sentence like this, leaving that unstated is completely normal.

Yes, when you are talking about laying/putting an object somewhere, класти is a very common and natural verb.

Here it fits well because a notebook is something you put into a backpack.

You may also meet other verbs depending on the situation:

• ставити = to put something standing/upright
• покласти = to put, lay down once/completely
• складати = to place/put together, stack, fold, etc. in some contexts

So кладу зошит у рюкзак is a very natural choice.

A helpful stress pattern is:

• Пі́сля уро́ку я кладу́ зо́шит у рюкза́к.

Approximate pronunciation:

• PIS-lya u-RO-ku ya kla-DU ZO-shyt u ryuk-ZAK

A few useful notes:

• я sounds like ya
• ю in рюкзак gives a ryu sound
• и in зошит is not the same as English ee; it is a more central vowel

You do not need perfect pronunciation right away, but learning stress early is very helpful.

Yes. In fact, that is probably the most natural reading without extra context.

Because кладу is an imperfective present, it can describe:

• what someone is doing now
• what someone usually does

So this sentence often means:

• After class, I put my notebook in my backpack.

That sounds like a routine or habit.

If you wanted to make right now clearer, context would usually do that, or you could add a time word such as:

• зараз = now

For example:

• Після уроку я зараз кладу зошит у рюкзак.

But on its own, the sentence is very naturally understood as a regular action.