Learn Hardcore German: Nach dieser Woche bin ich endlich wieder entspannt, weil das Projekt fertig ist. - After this week I am finally relaxed again because the project is finished.

Nach dieser Woche is a time expression (a prepositional phrase of time). In German you can put time expressions at the beginning of a sentence for emphasis or good style.

The structure is:

Time phrase (Vorfeld): Nach dieser Woche
Verb (position 2): bin
Subject: ich
Rest: endlich wieder entspannt, weil das Projekt fertig ist.

Why does the verb come before ich: bin ich instead of ich bin?

German main clauses require the conjugated verb in second position (V2 rule).

If you start with something other than the subject (here: Nach dieser Woche), that element counts as “position 1”, so the verb must come next:

Normal order: Ich bin entspannt.
With time phrase first: Nach dieser Woche bin ich entspannt.

The meaning is the same; only the emphasis changes slightly.

What exactly is entspannt here – a verb or an adjective?

Entspannt is formally the past participle of the verb entspannen, but in this sentence it’s used as a predicative adjective (a description after sein):

ich bin entspannt = I am relaxed.

Like in English I am tired / I am relaxed, German uses sein + adjective/participle to describe a state.
As a predicative adjective, entspannt does not change its ending for gender or number here.

What nuance does endlich wieder have? Could I just say endlich?

endlich = finally, at last (after a long wait).
wieder = again/once more.

Endlich wieder entspannt suggests:

You were relaxed before,
then you were not relaxed for some time (because of the project),
and now, finally, you are relaxed again, like you used to be.

If you say only endlich entspannt, it focuses more on “relaxed at last,” without strongly hinting that this is a return to a previous normal state. Both are correct; the nuance is slightly different.

Why is it wieder entspannt and not entspannt wieder?

In German, modal/degree adverbs (like wieder, schon, noch, gern) usually come before the adjective they modify:

wieder entspannt (again relaxed)
schon müde (already tired)
noch wach (still awake)

Entspannt wieder would sound odd here and is not idiomatic in this meaning.

Why does weil das Projekt fertig ist have the verb ist at the end?

Weil introduces a subordinate clause (a dependent clause expressing a reason). In German subordinate clauses, the conjugated verb goes to the end of the clause:

Main clause: Das Projekt ist fertig. (verb in 2nd position)
Subordinate clause: … weil das Projekt fertig ist. (verb at the end)

This verb-final word order is standard after conjunctions like weil, dass, obwohl, wenn, etc.

Why is it present tense ist when the project is already finished? Shouldn’t it be past tense?

In German (and in English) you normally talk about a finished state using present tense + an adjective:

Das Projekt ist fertig. = The project is finished/complete.

This describes the current state of the project (now it stands in a finished condition).
If you wanted to emphasize the completion as an event, you could also say:

Das Projekt ist fertig geworden. / Das Projekt wurde fertiggestellt.

But for everyday language, ist fertig is completely natural to mean “is (now) finished.”

Could I say weil das Projekt fertig war instead of ist? What is the difference?

Yes, weil das Projekt fertig war is grammatically correct, but it shifts the time perspective:

weil das Projekt fertig ist:
Focus on the current state: the project is (now) finished, and that is why I am relaxed now.
weil das Projekt fertig war:
Focus more on the past situation: the project was finished at some (past) time, and in that past context I was relaxed.

In the given sentence, because you’re expressing a current feeling (bin ich endlich wieder entspannt), the present ist is the more natural choice.

Why is there a comma before weil?

German requires a comma between main clauses and subordinate clauses.

Main clause: Nach dieser Woche bin ich endlich wieder entspannt
Subordinate clause: weil das Projekt fertig ist

Whenever you introduce a subordinate clause with weil, dass, obwohl, wenn, etc., you separate it from the main clause with a comma.

What other words could replace weil, and how would the word order change?

Two common alternatives are denn and da:

denn (also “because”, more like a coordinating conjunction)
- Nach dieser Woche bin ich endlich wieder entspannt, denn das Projekt ist fertig.
- With denn, the clause after it is a main clause, so the verb stays in 2nd position: ist fertig, not fertig ist.
da (“since / as”, often more formal than weil)
- Da das Projekt fertig ist, bin ich nach dieser Woche endlich wieder entspannt.
- Da also introduces a subordinate clause, so the verb goes to the end: ist at the end.

Why is it das Projekt? What gender and case is that?

Projekt is a neuter noun in German:

nominative singular: das Projekt

In weil das Projekt fertig ist,

das Projekt is the subject of the subordinate clause,
so it is in the nominative case,
and it takes the article das because of its neuter gender.

Why use fertig here and not something like beendet or zu Ende?

All can express a similar idea, but fertig is the most neutral and common for projects, tasks, etc.:

Das Projekt ist fertig. – Very standard, everyday German.
Das Projekt ist beendet. – Slightly more formal, often used for official processes, contracts, events.
Das Projekt ist zu Ende. – Focuses on “it has come to an end”; works, but sounds a bit more like an event ending.

In casual speech about work, fertig is usually the natural choice.

Could I also say Ich bin nach dieser Woche endlich wieder entspannt, weil das Projekt fertig ist? Is that different?

Yes, that is also perfectly correct.

Nach dieser Woche bin ich endlich wieder entspannt, …
Ich bin nach dieser Woche endlich wieder entspannt, …

Both mean the same. The difference is emphasis and rhythm:

Starting with Nach dieser Woche highlights the time period more strongly.
Starting with Ich is more neutral and is default word order.

Grammatically, both are fine.