Після кожного уроку мені легше говорити.

Because після (after) requires the genitive case in Ukrainian.

So:

• кожен урок = each lesson (dictionary/basic form)
• після кожного уроку = after each lesson (genitive)

Both words change:

• кожен → кожного
• урок → уроку

This is very common in Ukrainian: certain prepositions force a specific case, and після always goes with the genitive.

Кожного уроку is in the genitive singular.

The noun урок is masculine singular, and the adjective/pronoun-like word кожний / кожен (each) must agree with it in:

• gender
• number
• case

So:

• nominative: кожен урок
• genitive: кожного уроку

This agreement is a core feature of Ukrainian grammar: adjectives and words like кожен match the noun they describe.

Мені is the dative case of я (I).

Here it means something like:

• to me
• for me

So the sentence is structured more like:

• After each lesson, to me it is easier to speak.

That sounds unnatural in English, but it is a very normal Ukrainian pattern.

Ukrainian often uses the dative with words like важко (difficult), легко (easy), холодно (cold), треба (necessary), etc.

Examples:

• Мені важко читати. = It is hard for me to read.
• Мені легко писати. = It is easy for me to write.

So мені does not mean me as a direct object here. It means for me / to me.

Легше is the comparative form of легко.

• легко = easily / easy
• легше = more easily / easier

So:

• Мені легко говорити. = It is easy for me to speak.
• Мені легше говорити. = It is easier for me to speak.

In this sentence, the idea is that after each lesson, speaking becomes easier than before, so the comparative makes sense.

Here легше is best understood as a predicative adverb / state word, not a normal adjective modifying a noun.

It is not describing a noun like easy lesson or easy task.
Instead, it describes the whole situation:

• мені легше говорити = it is easier for me to speak

This is a very common Ukrainian structure:

• Мені важко працювати.
• Йому цікаво вчитися.
• Нам добре тут.

So легше is functioning as part of an impersonal expression, not as a regular adjective attached to a noun.

Because the sentence means it is easier to speak, and after words like легше, важко, приємно, корисно, Ukrainian commonly uses the infinitive.

So:

• мені легше говорити = it is easier for me to speak
• literally: to me easier to speak

This is similar to English in meaning, even though the grammar is a bit different.

More examples:

• Мені важко зрозуміти. = It is hard for me to understand.
• Їй приємно бачити тебе. = It is pleasant for her to see you.

Because in the present tense, Ukrainian usually does not use a verb like is / are in sentences of this type.

English says:

• It is easier for me to speak.

Ukrainian simply says:

• Мені легше говорити.

The present-tense copula is normally omitted.

If you were talking about the past or future, a form of бути (to be) could appear:

• Мені було легше говорити. = It was easier for me to speak.
• Мені буде легше говорити. = It will be easier for me to speak.

But in the present, leaving it out is standard.

Because я is not needed here.

The idea is not I speak in the normal sense. The structure is:

• мені = for me
• легше = easier
• говорити = to speak

So the sentence is not built around a subject I + verb speak. It is built around the impersonal idea it is easier for me to speak.

That is why мені appears instead of я.

Yes. Ukrainian word order is flexible, though each order can feel slightly different in emphasis.

The neutral version here is:

• Після кожного уроку мені легше говорити.

Other possible orders include:

• Мені легше говорити після кожного уроку.
• Говорити мені легше після кожного уроку.

All of these can work, but the original sentence naturally puts the time phrase first: After each lesson...

So the original version sounds smooth and neutral.

Говорити means to speak / to talk and is the natural verb here for general speaking ability.

It is also imperfective, which fits the idea of an ongoing skill or general activity.

Compare:

• говорити = to speak / to be speaking / to talk in a general sense
• сказати = to say something once, to make a completed utterance

So:

• Мені легше говорити. = It is easier for me to speak.

This means speaking in general is becoming easier, not just saying one thing once.

A rough pronunciation guide for English speakers is:

PIS-lya KOZH-no-ho oo-RO-koo meh-NEE LEH-hshe ho-vo-RY-ty

A few notes:

• Після has a soft л sound: PIS-lya
• кожного is pronounced with h-like г: KOZH-no-ho
• легше has the cluster гш, which sounds roughly like LEH-hshe
• stress:
  • Пі́сля
  • ко́жного
  • уро́ку
  • мені́
  • ле́гше
  • говори́ти

If you want to sound more natural, pay special attention to the soft consonants and the Ukrainian г, which is usually not a hard English g.

Yes, that is a very natural English rendering of the same idea.

The Ukrainian sentence literally follows the pattern:

• After each lesson, for me it is easier to speak.

But in natural English, you could translate it as:

• After each lesson, it’s easier for me to speak.
• After each lesson, I speak more easily.
• After each lesson, speaking gets easier for me.

The first one is closest structurally, but all of them express the same core meaning.