Learn Hardcore German: Ich ignoriere den Lärm im Treppenhaus und lese weiter. - I ignore the noise in the stairwell and keep reading.

It takes dative when it describes a location (where something is).
It takes accusative when it describes movement towards something (where to).

Here, the noise is located in the stairwell (no movement), so you use dative:

im Treppenhaus = in dem Treppenhaus = in the stairwell (location).

What is the difference between im Treppenhaus and ins Treppenhaus?

im Treppenhaus = in dem Treppenhaus → dative → location
The noise is in the stairwell.
ins Treppenhaus = in das Treppenhaus → accusative → movement
I go into the stairwell.

So:

Ich höre Lärm im Treppenhaus. – I hear noise in the stairwell. (where)
Ich gehe ins Treppenhaus. – I go into the stairwell. (where to)

Why is it im Treppenhaus and not auf der Treppe?

Both are possible, but they mean slightly different things:

im Treppenhaus – in the stairwell as a space (the whole area: stairs, landings, walls).
auf der Treppe – on the actual steps of the stairs.

If the noise is generally coming from the stairwell area, im Treppenhaus is more natural.
If you want to stress that someone is physically on the steps, you could say auf der Treppe.

What does Treppenhaus mean exactly, and is it used everywhere in German?

Treppenhaus literally means “stair house”, i.e. stairwell: the area in a building where the stairs and landings are.

Regional notes:

In Germany, Treppenhaus is the standard word.
In Austria and parts of southern Germany, people often say Stiegenhaus instead.
In everyday English, it’s usually stairwell or stairway (depending on context).

What is the difference between Lärm, Geräusch, and Krach?

These all relate to “noise,” but with different nuances:

Lärm – noise that is loud and disturbing, usually negative.
den Lärm ignorieren – ignore the (annoying) noise.
Geräusch – a neutral sound; not automatically bad or loud.
ein seltsames Geräusch hören – hear a strange sound.
Krach – very loud noise / racket, often sudden or chaotic.
Was ist das für ein Krach? – What’s that racket?

In the sentence, den Lärm suggests it’s unpleasant, disturbing noise.

Why is it ignoriere and not ignorieren in this sentence?

Ignoriere is the 1st person singular present form of the verb ignorieren.

The infinitive is:

ignorieren – to ignore.

Conjugation in the present tense:

ich ignoriere
du ignorierst
er/sie/es ignoriert
wir ignorieren
ihr ignoriert
sie/Sie ignorieren

Since the subject is ich (I), you need ich ignoriere.

Why is the word order und lese weiter and not und weiter lese?

After und, you start a new main clause. In a main clause, German wants the finite verb in second position.

The second clause is effectively:

(Ich) lese weiter.

In coordination, you can drop the repeated subject:

Ich ignoriere den Lärm im Treppenhaus und (ich) lese weiter.

So:

und lese weiter – verb (lese) is in 2nd position (after und, which connects the clauses).
und weiter lese would put lese in 3rd position, which is wrong for a main clause.

Why is weiter at the end of the sentence?

Weiterlesen is a separable verb: weiter- (prefix) + lesen (to read).

In main clauses in the present tense:

The finite verb (conjugated part) goes to position 2.
The separable prefix goes to the end of the clause.

So:

Infinitive: weiterlesen – to continue reading
Main clause: ich lese weiter – I continue reading / I read on

That’s why you get:

… und lese weiter.
not
… und weiter lese.

Could I also say Ich lese weiter instead of … und lese weiter?

Yes. Both are correct:

Ich ignoriere den Lärm im Treppenhaus und lese weiter.
(I ignore the noise in the stairwell and keep reading.)
Ich ignoriere den Lärm im Treppenhaus, und ich lese weiter.
Also correct, just more explicit because you repeat ich.

Dropping the second ich is very common when the subject doesn’t change.

How is the German present tense here translated into English? Does ich ignoriere mean I ignore or I am ignoring?

German has only one present tense form, which covers both simple and progressive meanings in English.

Ich ignoriere den Lärm … can mean:

I ignore the noise … (habitual / general)
I am ignoring the noise … (right now)

The correct English translation depends on context. In this specific sentence, I’m ignoring the noise in the stairwell and keep reading is a natural choice.

Why does German use den Lärm (with the) when English often says just noise?

Article use is different in German and English.

English:

often uses no article for general notions: I ignore noise easily.

German:

more often uses a definite article, especially when it’s a concrete, specific instance:
- den Lärm – the actual noise you’re hearing right now.

So:

Ich ignoriere den Lärm im Treppenhaus.
literally: I ignore the noise in the stairwell.
In natural English you might also say: I ignore the noise coming from the stairwell…

What are the article forms for Lärm and Treppenhaus in different cases?

Lärm – masculine (der Lärm):

Nominative: der Lärm
Accusative: den Lärm
Dative: dem Lärm
Genitive: des Lärms

Treppenhaus – neuter (das Treppenhaus):

Nominative: das Treppenhaus
Accusative: das Treppenhaus
Dative: dem Treppenhaus
Genitive: des Treppenhauses

In the sentence:

den Lärm → accusative masculine (direct object)
im Treppenhaus → in dem Treppenhaus → dative neuter (location)

Could I say Ich überhöre den Lärm im Treppenhaus instead of Ich ignoriere den Lärm…?

You can say Ich überhöre den Lärm im Treppenhaus, but it has a slightly different nuance.

ignorieren – consciously ignore; you are aware of it and decide not to react.
überhören – literally “overhear” in the sense of not hearing something, often unintentionally or because something is drowned out.

So:

Ich ignoriere den Lärm … – I notice the noise but choose to ignore it.
Ich überhöre den Lärm … – I (supposedly) don’t hear the noise / fail to hear it, or I pretend not to hear it.

In your sentence, ignoriere fits better if the idea is a conscious decision to keep reading despite the noise.