Obwohl das Buch nicht vorgemerkt ist, gibt es keine Leihfristverlängerung.

Obwohl means although or even though. It introduces a subordinate clause.

So in:

Obwohl das Buch nicht vorgemerkt ist, ...

the speaker is setting up a contrast:
Although the book is not reserved, ...

A clause introduced by obwohl does not stand as the main statement; it gives background information that contrasts with what comes next.

Because obwohl introduces a subordinate clause, German sends the finite verb to the end of that clause.

Compare:

• Main clause: Das Buch ist nicht vorgemerkt.
• Subordinate clause: ..., obwohl das Buch nicht vorgemerkt ist.

This is one of the most important German word-order rules: in many subordinate clauses, the conjugated verb goes to the end.

The basic main-clause pattern is:

Es gibt keine Leihfristverlängerung.
= There is no loan extension.

But when a subordinate clause comes first, that whole clause takes up the first position in the sentence. German main clauses still keep the finite verb in second position, so the next clause begins with the verb:

• Obwohl das Buch nicht vorgemerkt ist, gibt es keine Leihfristverlängerung.

So this is not random inversion. It happens because the initial obwohl clause counts as position 1, and gibt must come next.

Das Buch is in the nominative case because it is the subject of the subordinate clause:

das Buch ... ist

You can think of it as the thing that is in the state of being reserved or not reserved.

In a library context, vorgemerkt usually means reserved, placed on hold, or requested in advance.

So:

• Das Buch ist vorgemerkt = The book is reserved / on hold
• Das Buch ist nicht vorgemerkt = The book is not reserved / not on hold

The verb behind it is vormerken, which often means to note down in advance, to reserve, or to place a hold on, depending on context.

It looks similar to a passive, but for learners it is often easiest to understand it here as a state:

• Das Buch ist vorgemerkt = The book is reserved

This is built with sein + past participle (vorgemerkt). In real usage, it often describes the book’s current status rather than emphasizing the action of someone reserving it.

So in this sentence, the important idea is simply the status: the book currently does not have a reservation on it.

German uses nicht and kein differently.

• nicht negates verbs, adjectives, participles, or whole ideas
• kein negates nouns that would otherwise have ein-type words or no article

Here:

• nicht vorgemerkt = not reserved
  (nicht negates vorgemerkt)

• keine Leihfristverlängerung = no loan extension
  (keine negates the noun Leihfristverlängerung)

So German is making two different kinds of negation:

1. the book is not reserved
2. there is no extension

Because in German, when you want to say no before a noun, you usually use kein.

• eine Leihfristverlängerung = a loan extension
• keine Leihfristverlängerung = no loan extension

Using nicht eine would sound very unusual here and would mean something different, more like not one specific extension in a contrastive context. The normal library-style wording is definitely keine Leihfristverlängerung.

It is a typical German compound noun:

• Leih = loan / lending
• Frist = period / deadline
• Verlängerung = extension

Together, Leihfristverlängerung means extension of the loan period, often naturally translated as renewal or loan extension.

German often packs several ideas into one long noun, and the final part usually tells you the basic category of the word. Here, the core noun is Verlängerung.

Because in German, a subordinate clause is normally separated from the main clause by a comma.

So:

Obwohl das Buch nicht vorgemerkt ist, gibt es keine Leihfristverlängerung.

That comma is required in standard German punctuation.

Yes. German allows both of these:

• Obwohl das Buch nicht vorgemerkt ist, gibt es keine Leihfristverlängerung.
• Es gibt keine Leihfristverlängerung, obwohl das Buch nicht vorgemerkt ist.

Both are grammatical. The difference is mostly about emphasis and flow.

When the obwohl clause comes first, it sets up the contrast immediately. When it comes second, the main message comes first.

Because keine is already acting like the article here.

Compare:

• eine Leihfristverlängerung = a loan extension
• keine Leihfristverlängerung = no loan extension

So keine fills the same slot that eine would fill. You do not add another article.

It has two parts:

1. Subordinate clause introduced by obwohl
   Obwohl das Buch nicht vorgemerkt ist

2. Main clause
   gibt es keine Leihfristverlängerung

A helpful structural view is:

• Obwohl
  • subject + other elements + verb
• then main clause with the finite verb in second position overall

So the sentence is a very good example of two important German rules at once:

• subordinate clause verb at the end
• main clause verb second, even after an opening subordinate clause