Όποιος κάνει το καθημερινό του μάθημα, μαθαίνει πιο γρήγορα.

Όποιος is an indefinite / generalizing pronoun meaning whoever, anyone who.

So the first part:

• Όποιος κάνει το καθημερινό του μάθημα
  = Whoever does their daily lesson / Anyone who does their daily lesson

By contrast:

• ποιος; = who? (used only in questions)

Examples:

• Ποιος κάνει το μάθημα; = Who is doing the lesson? (direct question)
• Όποιος κάνει το μάθημα, μαθαίνει. = Whoever does the lesson learns. (general statement, not a question)

Grammatically, όποιος is masculine singular, but in modern Greek it is often used as a generic form meaning whoever / anyone, not just males.

Greek has:

• όποιος (masculine, singular)
• όποια (feminine, singular)
• όποιο (neuter, singular)

In neutral, general statements, speakers usually choose the masculine as the default generic:

• Όποιος διαβάζει, μαθαίνει.
  = Whoever studies, learns. (applies to everyone)

If you wanted to be explicitly inclusive in written language, you could write:

• Όποιος ή όποια κάνει το καθημερινό μάθημα…
  (whoever – male or female – does the daily lesson…)

But in everyday speech, just όποιος is completely normal and understood as anyone who.

The sentence has two parts:

1. Όποιος κάνει το καθημερινό του μάθημα,
   = subordinate clause (condition / premise): Whoever does their daily lesson,
2. μαθαίνει πιο γρήγορα.
   = main clause (result): learns faster.

In Greek, when a subordinate clause (Όποιος κάνει το καθημερινό του μάθημα) comes first, it is normally followed by a comma before the main clause μαθαίνει πιο γρήγορα.

If you reverse the order, you usually omit the comma:

• Μαθαίνει πιο γρήγορα όποιος κάνει το καθημερινό του μάθημα.
  (no comma needed)

Even though όποιος refers to any person in general, it is grammatically singular. So the verb must also be singular:

• Όποιος κάνει… μαθαίνει…
  (όποιος = singular → μαθαίνει = 3rd person singular)

This is similar to English structures like:

• Anyone who studies learns faster.
  (anyone is grammatically singular, so we say learns, not learn)

So the singular μαθαίνει is required by the grammar.

The phrase το καθημερινό του μάθημα literally means his daily lesson or their daily lesson. Word by word:

• το – definite article, neuter, singular, accusative
• καθημερινό – adjective καθημερινός (daily), neuter, singular, accusative
• του – possessive clitic pronoun, his / her / its / their (here: his / their)
• μάθημα – noun, neuter, singular, accusative (lesson, class, exercise)

So the order is:

[article] + [adjective] + [possessive pronoun] + [noun]
το καθημερινό του μάθημα = his daily lesson

του is a clitic possessive pronoun in the genitive, 3rd person singular. It usually means:

• his (masculine)
• its (neuter)
• but in generic sentences, it often corresponds to one’s / their in English

In this sentence:

• Όποιος κάνει το καθημερινό του μάθημα…
  = Whoever does their daily lesson…

So του refers back to όποιος:

• όποιος → του
  (whoever → their)

If you changed the person, you would also change του:

• Κάνω το καθημερινό μου μάθημα. = I do my daily lesson.
• Κάνεις το καθημερινό σου μάθημα. = You do your daily lesson.
• Κάνουν το καθημερινό τους μάθημα. = They do their daily lesson.

In Greek, κάνω μάθημα is a very common collocation. Depending on context, it can mean:

• do one’s lesson / do one’s homework
• have a lesson / have class
• teach a lesson (for a teacher)

Here, it clearly means:

• Όποιος κάνει το καθημερινό του μάθημα…
  ≈ Whoever does their daily studying / homework every day…

You could also say:

• Όποιος διαβάζει κάθε μέρα, μαθαίνει πιο γρήγορα.
  = Whoever studies every day learns faster.

That sounds even more like “study” rather than “do a specific lesson”.
But κάνει το καθημερινό του μάθημα is perfectly natural to mean does their daily lesson/study routine.

πιο γρήγορα means faster or more quickly.

Structure:

• γρήγορα – adverb quickly / fast (from the adjective γρήγορος = fast, quick)
• πιο – more, used to form comparatives of adjectives and adverbs

So:

• γρήγορα = quickly
• πιο γρήγορα = more quickly / faster

In Greek, many comparatives are formed with πιο + adjective/adverb:

• πιο αργά = more slowly
• πιο καλά = better
• πιο εύκολα = more easily

There is also a more “traditional” comparative form γρηγορότερα, but in everyday modern Greek πιο γρήγορα is more common.

Greek is a pro‑drop language: subject pronouns are usually omitted when the subject is clear from the context or from the verb ending.

In this sentence, the subject is already clear:

• Όποιος κάνει το καθημερινό του μάθημα, μαθαίνει πιο γρήγορα.

The subject of μαθαίνει is the same όποιος from the first clause, so adding αυτός would be redundant and normally sounds unnatural:

• ✗ Όποιος κάνει το καθημερινό του μάθημα, αυτός μαθαίνει πιο γρήγορα.
  (only used for strong emphasis, e.g. in contrast to someone else)

So the natural version leaves the subject pronoun out.

Yes, Greek word order is relatively flexible. You can move the clauses around without changing the basic meaning.

Original:

• Όποιος κάνει το καθημερινό του μάθημα, μαθαίνει πιο γρήγορα.

Possible variants:

• Μαθαίνει πιο γρήγορα όποιος κάνει το καθημερινό του μάθημα.
  (main clause first; no comma)

• Όποιος το καθημερινό του μάθημα κάνει, μαθαίνει πιο γρήγορα.
  (more marked/emphatic: stress falls on καθημερινό του μάθημα)

All of these mean essentially:

• Whoever does their daily lesson learns faster.

The original order is the most neutral and natural for a proverb‑like, general statement.