Mein Bruder mag den Altbau mehr als den Neubau, obwohl der Neubau einen Aufzug hat.

Mag is the 3rd person singular present tense of mögen.

Because the subject is mein Bruder (my brother), German uses the er/sie/es form:

• ich mag
• du magst
• er/sie/es mag

So Mein Bruder mag ... means My brother likes ...

Also, mögen is an irregular verb, which is why you get mag rather than something more predictable.

Because mein Bruder is the subject of the sentence, so it is in the nominative case.

Bruder is masculine singular, and with a possessive word like mein, the nominative masculine form is:

• mein Bruder

If it were a direct object, then you would get:

• meinen Bruder

So here:

• Mein Bruder = the person doing the liking

Because Altbau is the direct object of mag, and mögen takes the accusative case.

Altbau is masculine, so:

• nominative: der Altbau
• accusative: den Altbau

That is why German says:

• Mein Bruder mag den Altbau ...

not der Altbau.

Because it is still part of the comparison with the object of mag.

The full idea is:

• My brother likes the old building more than the new building.

In German, the second noun keeps the role it has in the comparison. Since den Altbau is an accusative object, den Neubau is also accusative here:

• den Altbau mehr als den Neubau

So als itself is not forcing den. The accusative comes from the fact that Neubau is being compared as another object of mag.

Because in the obwohl clause, der Neubau is now the subject:

• obwohl der Neubau einen Aufzug hat

Here, the new building is the thing that has the elevator, so it must be in the nominative case:

• nominative masculine: der Neubau

So the sentence uses both forms of the same noun for different grammatical jobs:

• den Neubau = object
• der Neubau = subject

Because Aufzug is the direct object of hat, and haben takes the accusative case.

Aufzug is masculine, so:

• nominative: ein Aufzug
• accusative: einen Aufzug

That is why the sentence says:

• einen Aufzug hat

Mehr als means more than.

In this sentence, it compares how much the brother likes two things:

• den Altbau mehr als den Neubau
• literally: the old building more than the new building

So the structure is:

• jemanden/etwas mehr mögen als ...
• to like someone/something more than ...

It is a very normal way to make a comparison.

Yes. A very natural alternative is:

• Mein Bruder mag den Altbau lieber als den Neubau.

Using lieber often sounds especially natural when talking about preference between two options.

So:

• mehr als = correct
• lieber als = also correct, and often very idiomatic

Both are possible, though lieber is often what learners hear first in preference sentences.

Because obwohl introduces a subordinate clause, and in German subordinate clauses send the conjugated verb to the end.

So:

• main clause: Mein Bruder mag den Altbau ...
• subordinate clause: obwohl der Neubau einen Aufzug hat

This is a key German word-order rule:

• obwohl, weil, dass, wenn, etc. usually send the verb to the end.

That is why you get:

• obwohl der Neubau einen Aufzug hat

not:

• obwohl der Neubau hat einen Aufzug

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

So the comma in

• ..., obwohl der Neubau einen Aufzug hat

is required.

This is one of the big punctuation differences from English: German uses commas very consistently to mark subordinate clauses.

Yes. You can also say:

• Obwohl der Neubau einen Aufzug hat, mag mein Bruder den Altbau mehr als den Neubau.

That is completely correct.

But notice what happens in the main clause after the subordinate clause comes first: the conjugated verb must still stay in second position, so you get:

• ..., mag mein Bruder ...

not:

• ..., mein Bruder mag ...

This is another important German word-order pattern.

A few useful things:

• They are compound nouns:
  • Alt
    • Bau
  • Neu
    • Bau
• German writes such compounds as one word.
• They are capitalized because they are nouns.
• Their gender is masculine because the final part, Bau, is masculine.

So:

• der Altbau
• der Neubau

This is a very common German pattern: the last part of a compound usually determines the gender and basic grammatical behavior.