Learn Hardcore Turkish: Kanyonun derinliklerinde, güneş ışığını takip ederek ilerleyen gezgin grupları vardı. - There were groups of travelers advancing by following the sunlight in the depths of the canyon.

Kanyonun = kanyon (canyon) + genitive suffix -un (“of the canyon”)
derinliklerinde = derinlik (depth) + plural -ler
- 3rd-person possessive+locative -inde (“in its depths”)
  Altogether: “in the depths of the canyon.”

Why is güneş ışığını in the accusative case, and what would happen if we left off the suffix?

güneş ışığını = güneş ışığı (sunlight) + accusative -nı (after vowel harmony becomes -nı/ -ni/ -nu/ -nü)
We use accusative because the sunlight is a specific object being tracked. Without -nı you’d say güneş ışığı, which sounds indefinite (“sunlight” in general) rather than “the sunlight” they were following.

What does the suffix -erek in takip ederek indicate?

-erek is an adverbial participle (gerund) suffix meaning “by …-ing” or “while …-ing.”
takip ederek = “by following” or “following (and thus).” It links the action of tracking the sunlight to their movement.

What is ilerleyen, and how is it formed?

ilerleyen comes from the verb ilerlemek (“to advance, to move forward”) + present active participle suffix -en, so it means “(the one) moving forward” or “advancing.” It functions as a verbal adjective modifying gezgin grupları.

Why is takip ederek ilerleyen placed before gezgin grupları, and what is this structure called?

In Turkish, participle phrases (verbal adjectives) precede the noun they modify. Here, takip ederek ilerleyen is a participial modifier (a kind of relative clause) describing gezgin grupları:
“the traveler groups that were moving forward by following the sunlight.”

What does vardı express here, and how would you say it in the present tense?

vardı is the past-tense form of the existential verb var (“there is/are”). It means “there were.”
In the present tense you’d say var:
– Kanyonun derinliklerinde güneş ışığını takip ederek ilerleyen gezgin grupları var.
(“Here in the canyon’s depths there are traveler groups moving forward by following the sunlight.”)

Why is the main verb vardı at the end of the sentence?

Turkish is an SOV (subject-object-verb) language. Even existential constructions place the verb at the end. Everything that describes or modifies the subject comes before it.

Why is there a comma after Kanyonun derinliklerinde?

The comma sets off the initial adverbial phrase (“in the depths of the canyon”) for clarity. Long fronted adverbials are often followed by a comma in written Turkish.

How would you say “in the depths of the canyons” (plural “canyons”)?

Pluralize kanyon with -lar plus genitive:
Kanyonların derinliklerinde
(= “in the depths of the canyons”)

Could you simplify takip ederek ilerleyen to takip eden? What’s the difference?

Yes, you could say güneş ışığını takip eden gezgin grupları vardı, which literally means “there were traveler groups that follow(ed) the sunlight.”
Difference in nuance:

takip eden is a simple attributive participle (“those who follow”).
takip ederek ilerleyen adds the manner “by following (the light), they progressed,” emphasizing how they moved.