A füzetembe tollal írok, a jegyzetet pedig később újra elolvasom.

Because Hungarian often builds several pieces of meaning into a single noun form.

füzetembe breaks down like this:

• füzet = notebook
• -em = my
• -be = into

So füzetembe literally means into my notebook.

This is very normal in Hungarian. Where English uses separate words, Hungarian often uses a stem plus endings.

With ír (to write), Hungarian very often uses the direction/target idea: you write into a notebook, onto paper, into a book, and so on.

So:

• a füzetembe írok = I write into my notebook
• a füzetemben írok would sound more like emphasizing location, I am writing in my notebook

In practice, with writing, -ba/-be is very common because the text is being put into the notebook as a result.

Because Hungarian can use a definite article even with possessed nouns.

So:

• a füzetembe = into my notebook
• a könyvem = my book
• a barátom = my friend

This is different from English, where the my notebook is impossible. In Hungarian, the article and the possessive ending can appear together quite naturally.

tollal is the instrumental form of toll (pen), and it means with a pen.

The ending -val/-vel means with / by means of.

So:

• toll = pen
• tollal = with a pen

It shows the instrument used for writing.

Because the ending -val/-vel changes after many consonants.

With words ending in a consonant, the v often disappears and the final consonant gets doubled in pronunciation/spelling:

• toll + val → tollal
• kéz + vel → kézzel
• vonat + val → vonattal

So tollal is the regular result of adding -val to toll.

That is the accusative ending, which marks the direct object.

• jegyzet = note / set of notes
• jegyzetet = the note / the notes (as the thing being read)

Hungarian usually marks direct objects explicitly with -t. The vowel before it can vary, so here you get -et.

Because the object is definite: a jegyzetet.

Hungarian verbs have two main conjugation patterns:

• indefinite conjugation: used when there is no definite object
• definite conjugation: used when the object is definite

Here the speaker is reading a jegyzetet (the note(s)), so the verb must be in the definite form:

• elolvasok = I read through / I will read through something nonspecific
• elolvasom = I read through it / I will read the specific thing

So elolvasom matches the definite object.

It gives the idea of reading through / finishing reading.

Compare:

• olvasom = I am reading it / I read it
• elolvasom = I read it through, I finish reading it

So újra elolvasom is not just I read it again, but more specifically I read it through again or I reread it.

pedig is a connector with a nuance like:

• and
• while
• whereas
• as for ...
• on the other hand

Its exact English translation depends on context. Here it helps link the two parts and slightly shifts attention to the second one:

• A füzetembe tollal írok, a jegyzetet pedig később újra elolvasom.

A natural sense is something like: I write in my notebook with a pen, and then/as for the notes, I reread them later.

So pedig often adds a mild contrast or topic shift, not necessarily a strong opposition.

Because újra (again) is an adverb, and Hungarian often places adverbs before the verb.

So:

• újra elolvasom = I reread it / I read it again

This is a very normal position. Hungarian is fairly flexible, but placing újra before the verb is natural and common.

Yes. Hungarian word order is much more flexible than English word order, and it often shows topic, focus, or emphasis rather than just grammatical roles.

In this sentence:

• A füzetembe sets up one topic/frame: as for my notebook / in my notebook
• tollal right before írok can sound slightly emphatic: with a pen
• a jegyzetet pedig shifts to the second topic: as for the note(s), ...

So the sentence is not just about grammar; it also reflects how the speaker organizes the information.

Other orders are possible, but they may sound more neutral or put emphasis in different places. Hungarian word order often answers the question What is being highlighted here?

Because Hungarian and English do not always use singular and plural in exactly the same way.

jegyzet is formally singular here, but depending on context it can refer to:

• a single note
• a written note
• a set of notes

So even if English translation uses notes, Hungarian may still use jegyzetet in the singular. The exact choice depends on what the speaker means in context.