Learn Hardcore Turkish: Kütüphane kalabalık olsa bile burada ders çalışacağız. - Even if the library is crowded, we will study here.

-sa bile strongly suggests “even if,” often regardless of whether the condition is true: Kütüphane kalabalık olsa bile... (“even if the library is crowded...”).
-sa da often reads as “although/even though,” implying the condition is (or can be taken as) true: Kütüphane kalabalık olsa da...
rağmen means “despite/although” and needs a noun/nominalized form: Kütüphane kalabalık olmasına rağmen... All three are natural; -sa bile adds a bit more “even if” flavor.

Where is the verb “is” in Kütüphane kalabalık? Why isn’t there a separate verb?

In Turkish, in simple present statements with adjectives/nouns, the copula “to be” is usually zero in 3rd person: Kütüphane kalabalık = “The library is crowded.” When you need tense/mood (like a conditional), you use ol-: kalabalık olsa (“if it is crowded”).

Why is it Kütüphane kalabalık, not Kütüphanede kalabalık?

Because the library is the subject. Kütüphane kalabalık = “The library is crowded.”
Kütüphanede kalabalık is possible only if kalabalık is used as a noun (“a crowd”), as in “There is a crowd at the library.” Then you’d be saying: Kütüphanede kalabalık olsa bile... (“Even if there is a crowd at the library...”). That’s a slightly different nuance.

Can I say kalabalık bile olsa instead of kalabalık olsa bile?

Yes. Bile generally follows the word it emphasizes, so kalabalık bile olsa places “even” directly on “crowded.” Both kalabalık olsa bile and kalabalık bile olsa are common and natural here; the meaning difference is minimal.

Can I put the main clause first?

Yes: Burada ders çalışacağız, kütüphane kalabalık olsa bile.
Turkish often places the subordinate clause first to set the scene, but either order works.

What does burada add, and could I say kütüphanede instead?

Burada = “here” (locative). It points to the current/previously understood place. If you want to be explicit, you can say kütüphanede:
Kütüphane kalabalık olsa bile kütüphanede ders çalışacağız.
If context already makes “here (at the library)” clear, burada is perfect.

What exactly is ders çalışmak? Why not just çalışmak?

Ders çalışmak is the idiomatic way to say “to study (schoolwork).”

çalışmak on its own primarily means “to work (at a job).”
Students do use çalışmak to mean “study,” but ders çalışmak is unambiguous.

How is çalışacağız formed and pronounced?

Formation:

stem: çalış-
future: -acak/-ecek (here -acak by vowel harmony) → çalışacak-
1st person plural: -ız → merges to çalışacağız

The ğ is a soft g; it lengthens/smooths the preceding vowel rather than making a hard sound. Roughly pronounced “cha-lɯ-sha-jaz.”

Why use the future tense here? Could I say çalışırız or çalışıyoruz instead?

çalışacağız = a plan/intention: “we will study (here).”
çalışırız = habitual or a firm decision/guarantee: “we (would) study (here)” or “we study here (as a rule), even if...”
çalışıyoruz = present/ongoing: with olsa bile, it can imply a current general practice: “Even if the library gets crowded, we (still) study here.” Choose the tense for the nuance you want.

How do I negate the sentence?

Negate the main verb: çalışmayacağız.
Example: Kütüphane kalabalık olsa bile burada ders çalışmayacağız (“Even if the library is crowded, we won’t study here”).
To negate the condition: kalabalık olmasa bile = “even if it’s not crowded.” You don’t say kalabalık değil olsa; use olmasa (negated ol-) for subordinate moods.

Is a comma required after the concessive clause?

Optional. Many writers add one for readability:
Kütüphane kalabalık olsa bile, burada ders çalışacağız.
Short clauses often omit it without issue.

Can I say this with rağmen instead?

Yes: Kütüphane kalabalık olmasına rağmen burada ders çalışacağız.
Here olmasına is the nominalized+dative form required by rağmen.

Any small tweaks to intensify or vary the meaning?

Add intensity: Kütüphane çok kalabalık olsa bile... (“even if it’s very crowded...”)
Alternative concessive: Kütüphane kalabalık da olsa... (similar to -sa bile)
Using “here” as subject: Burası kalabalık olsa bile burada ders çalışacağız.