Bu dersi düzenli tekrar edersen, gerçekten ilerlediğini göreceksin.

In Turkish, when a specific thing is the direct object of the verb, it usually takes the accusative case suffix.

• ders = lesson / course (basic form)
• ders-i = the lesson / this particular course (as a direct object)

In this sentence, you are talking about a specific lesson/course (probably the one you are doing now), and you are repeating this particular lesson, not lessons in general. So Turkish marks it as a definite object:

• Bu dersi tekrar edersen = If you repeat this lesson
• Ders tekrar ediyorum = I am repeating lesson(s) (in general, not a specific one)

Düzenli literally means regular / orderly, and as in many languages, adjectives can be used adverbially in Turkish.

Here:

• düzenli tekrar edersen ≈ if you repeat (it) regularly

Grammatically:

• düzenli is originally an adjective, but here it functions like an adverb (regularly).
• This is very common in Turkish: adjectives are often used directly as adverbs.

You can also say:

• Bu dersi düzenli olarak tekrar edersen
• Bu dersi düzenli bir şekilde tekrar edersen

These all mean essentially the same thing.
Düzenli alone is the most natural and concise in everyday speech.

Tekrar etmek is a light verb construction:

• tekrar = repetition (noun)
• etmek = to do / to make

Together: tekrar etmek = to repeat.

Even though it is written as two words, it behaves like a single verb (you conjugate etmek):

• tekrar ederim = I repeat
• tekrar ediyorsun = you are repeating
• tekrar edersen = if you repeat

You can also use tekrarlamak, which is a single-word verb:

• Bu dersi düzenli tekrarlarsan, ...

In most contexts, tekrar etmek and tekrarlamak are interchangeable, with only a slight style difference (both are very common; many speakers don’t feel a difference at all here).

Edersen is the conditional form of etmek (to do):

• et- = verb stem
• -er = aorist (general/present) marker
• -sen = 2nd person singular conditional ending (if you ...)

So edersen ≈ if you do / if you make.

Because etmek is part of the compound verb tekrar etmek, tekrar edersen together means:

• tekrar edersen = if you repeat (it)

Note:
Compare:

• tekrar edersin = you repeat (general/habitual fact)
• tekrar edersen = if you repeat (conditional)

In Turkish, personal pronouns (ben, sen, o, etc.) are often dropped, because the verb ending already shows the person.

• görecek-sin → the -sin ending means you (singular, informal).

So:

• Gerçekten ilerlediğini göreceksin.
  Literally: You-will-see that you-have-progressed.

Adding sen is grammatically possible but usually unnecessary and sometimes sounds emphatic:

• Sen gerçekten ilerlediğini göreceksin.
  This emphasizes you, like: You will see that you have progressed (as opposed to someone else).

Göreceksin is the future tense, 2nd person singular of görmek (to see):

• gör- = verb stem (to see)
• -ecek = future tense suffix
• -sin = 2nd person singular ending

So:

• göreceksin = you will see

From this single word, we know:

• Tense: future
• Person: 2nd person
• Number: singular
• Politeness: informal (you-talking-to-one-person)

İlerlediğini is a subordinate clause turned into a noun phrase, functioning as the object of göreceksin.

Breakdown:

• ilerle- = to advance / to progress
• -dik = nominalizer (turns verb into a clause like that X did)
• -in = 2nd person singular possessive (your / that you)
• -i = accusative case (because this whole clause is the object of göreceksin)

With sound changes:

• ilerle + dik + in + i → ilerlediğini

Meaning:

• (senin) ilerlediğin(i) = that you have progressed / your having progressed

So in the full sentence:

• gerçekten ilerlediğini göreceksin
  = you will see that (you) have really progressed.

It looks like a past form because Turkish uses this -dik structure to refer to a completed or existing state at some reference time, and that reference time here is in the future (when you see the result).

Turkish uses -dik (here realized as -diğ-) to create object clauses that describe a completed or factual event relative to another time.

In this sentence:

• Main time: future → göreceksin (you will see)
• Inner event: completed by that future time → ilerlediğini (that you have progressed)

So the logic is:

• In the future, you will see the fact that by then you have already progressed.

A more literal English feeling would be:

• You will see that you have really made progress.

Using ilerleyeceğini (that you will progress) would change the meaning:

• Bu dersi düzenli tekrar edersen, gerçekten ilerleyeceğini göreceksin.
  = If you repeat this lesson regularly, you will see that you will (eventually) progress.

The original sentence focuses on observing the already achieved progress.

Turkish has relatively flexible word order, especially inside clauses, but there are preferences.

The original:

• Bu dersi düzenli tekrar edersen, gerçekten ilerlediğini göreceksin.

Some natural variations:

• Bu dersi düzenli tekrar edersen, ilerlediğini gerçekten göreceksin.
  (emphasis slightly more on really seeing it)

• Bu dersi gerçekten düzenli tekrar edersen, ilerlediğini göreceksin.
  (emphasis that you do it really regularly)

Less natural or awkward:

• Bu dersi düzenli tekrar edersen, göreceksin gerçekten ilerlediğini.
  Grammatically possible but sounds marked / poetic / conversationally odd.

General rules:

• The finite verb (here göreceksin) usually stays near the end of its clause.
• Adverbs like gerçekten can move, mostly changing emphasis, not core meaning.

To address you (plural or polite), you change the verb endings to 2nd person plural:

• Bu dersi düzenli tekrar ederseniz, gerçekten ilerlediğinizi göreceksiniz.

Changes:

• ederseniz = if you (pl./polite) repeat
• ilerlediğinizi = that you (pl./polite) have progressed
  (still: ilerle- + -dik + -niz + -i)
• göreceksiniz = you (pl./polite) will see

Everything else stays the same.

Yes, that is grammatically correct:

• Bu dersi tekrar edersen, gerçekten ilerlediğini göreceksin.
  = If you repeat this lesson, you will really see that you have progressed.

Without düzenli, it just means if you repeat it, maybe once or a few times; there is no idea of regularity or consistency.

With düzenli, the sentence emphasizes:

• habit / routine / consistency → repeating the lesson regularly over time is what leads to progress.

Turkish has three basic demonstratives:

• bu = this (near the speaker)
• şu = that (a bit further away / not immediately present / often: that [previously mentioned] thing)
• o = that (far from both speaker and listener / more abstract or already known)

In practice:

• Bu dersi = this lesson / this course (the one we are doing / looking at now)
• Şu dersi = that lesson there / that one we mentioned / that over there
• O dersi = that lesson (more distant in time, space, or context)

In language-learning contexts, Bu dersi is very natural for this lesson (you are now working on).