Learn Hardcore Icelandic: Húsið þar sem amma mín býr er rólegt og gamalt. - The house where my grandmother lives is quiet and old.

So húsið means the house in the nominative/accusative singular, neuter. There is no separate word for the in this sentence; it’s built into húsið.

How does þar sem work? Is it the same as English where or that?

Þar sem is a fixed combination:

þar = there (an adverb of place)
sem = a general relative word (that/which/who)

Together, þar sem usually means where in the sense of “in the place where …”.

In Húsið þar sem amma mín býr…, the part þar sem amma mín býr is a relative clause describing the house:

húsið þar sem amma mín býr ≈ the house where my grandmother lives

So here þar sem functions like English where, not like a demonstrative that.

Why is the word order amma mín býr and not býr amma mín?

The phrase þar sem amma mín býr is a subordinate clause (a relative clause). In Icelandic subordinate clauses, the normal order is:

Subject – Verb – (rest)

So:

amma mín (subject)
býr (verb)

Býr amma mín would sound like a yes/no question (“Does my grandmother live…?”) or like a special kind of inversion, so it would be wrong in this relative clause.

Why is there no comma before þar sem?

Modern Icelandic punctuation normally omits commas before relative clauses introduced by sem and þar sem, unless there is a special pause or parenthetical effect.

So:

Húsið þar sem amma mín býr er rólegt og gamalt.
(no comma)

is the standard way to write it. This is similar to English “The house where my grandmother lives is quiet and old”, which also normally has no comma.

Why does the possessive mín come after amma instead of before it?

In Icelandic, the usual order with the common “weak” possessive pronouns (mín, þín, hans, hennar, okkar, ykkar, þeirra) is:

noun + possessive

So:

amma mín = my grandmother
(literally grandmother my)

Some key points:

amma mín is already definite; you do not add an article:
*húsið þar sem mín amma býr is not normal Icelandic.
mín agrees with amma: feminine, singular, nominative.
Putting mín before the noun (mín amma) is possible only in special emphatic or stylistic contexts; in everyday speech, amma mín is the natural form.

Why are the adjectives rólegt and gamalt ending in -t?

The subject of the sentence is húsið, which is:

neuter
singular
nominative (subject case)

In Icelandic, adjectives must agree with the noun they describe in gender, number, and case—even when they come after the verb (predicate adjectives):

masculine: rólegur, gamall
feminine: róleg, gömul
neuter: rólegt, gamalt

Since húsið is neuter singular nominative, the adjectives must also be neuter singular nominative:

Húsið … er rólegt og gamalt.
The house … is quiet and old.

Could it be rólegur og gamall instead? When would you use that?

Rólegur og gamall is the masculine form, so you would use it if the subject is a masculine noun, for example:

Kötturinn er rólegur og gamall.
The (male) cat is quiet and old.

For húsið (neuter), using rólegur og gamall would be ungrammatical. You must keep rólegt og gamalt to agree with the neuter noun húsið.

What is the difference between býr and other verbs for “live”, like lifir?

Icelandic distinguishes two main ideas of live:

búa → býr
= live, reside, dwell (somewhere)
Used for where someone lives (address, town, house).
- Amma mín býr í þessu húsi. – My grandmother lives in this house.
lifa → lifir
= live, be alive, stay alive, survive
Used for being alive, not for residence.
- Hún lifir enn. – She is still alive.

In your sentence, we are talking about where the grandmother lives, so býr (from búa) is the only natural choice.

Why is amma in the nominative case here?

Inside the clause þar sem amma mín býr, the phrase amma mín is the subject of the verb býr (lives).

In Icelandic:

The subject of a normal active verb is usually in the nominative case.

So we use the base form amma (nominative), not ömmu (which would be accusative or dative).

Compare:

Ég heimsæki ömmu mína. – I visit my grandmother.
Here ömmu mína is an object, so it’s accusative, not nominative.

Could you also say Húsið sem amma mín býr í? If so, what’s the difference?

Yes, you can, and it’s natural Icelandic:

Húsið þar sem amma mín býr ≈ The house where my grandmother lives
Húsið sem amma mín býr í ≈ The house (that) my grandmother lives in

Differences:

þar sem behaves like where (place adverb + relative word).
With just sem, you use the preposition í at the end (býr í), just like English lives in.
Both are correct and common. Þar sem often sounds a bit more “neatly” place-focused (like English where), while sem … í is more like everyday that … in.

How does the main verb er fit into Icelandic word order rules?

Icelandic main clauses usually obey a V2 rule: the finite verb comes in the second position in the clause.

In your sentence, the structure of the main clause is:

Húsið þar sem amma mín býr – one long subject phrase (this entire chunk counts as position 1)
er – the finite verb vera (to be)
rólegt og gamalt – the rest of the predicate

So even though a lot of words come before er, they form a single subject unit. The verb er is still in the second slot, so the V2 rule is satisfied.