Ástin er sterk.

Ástin means the love. Icelandic usually adds the definite article to the end of the noun instead of using a separate word like English the.

So:

ást = love
ástin = the love

In this sentence, Ástin er sterk, the subject is specific: the love is strong.

Ást is a feminine noun. Gender matters in Icelandic because adjectives often change form to match the noun’s gender, number, and case.

Here, ástin is:

feminine
singular
nominative (because it is the subject)

That is why the adjective appears as sterk.

The adjective must agree with the noun it describes.

The noun ástin is feminine singular nominative, so the adjective takes the feminine singular nominative form:

sterkur = masculine
sterk = feminine
sterkt = neuter

So:

Ástin er sterk = correct
because ástin is feminine.

Er means is. It is the present singular form of the verb vera, which means to be.

A few common forms are:

ég er = I am
þú ert = you are
hann/hún/það er = he/she/it is

So in Ástin er sterk, er simply links the subject ástin with the description sterk, just like English is.

Yes. This is the normal and most straightforward word order:

subject + verb + complement

So:

Ástin = subject
er = verb
sterk = adjective complement

This is very similar to English Love is strong or The love is strong.

Icelandic can sometimes change word order for emphasis, style, or in questions, but this sentence is the standard neutral order.

It is in the nominative case because it is the subject of the sentence.

In Icelandic, the subject of a basic sentence is usually nominative. Since ástin is the thing being described as strong, it appears in the nominative.

That also helps explain why the adjective is in the nominative form too.

A rough English-friendly guide is:

OWS-tin er sterhk

A few helpful points:

Á is pronounced roughly like ow in now.
st in ástin is pronounced clearly.
er is short, like air said quickly, though not exactly the same.
r in Icelandic is usually a rolled or tapped r.
sterk has a clear k at the end.

A more approximate breakdown is:

Ástin → OWS-tin
er → ehr
sterk → sterk

Pronunciation varies a little by speaker, but this will get you close.

Yes, but it means something slightly different.

Ást er sterk = Love is strong / Love in general is strong
Ástin er sterk = The love is strong / The specific love is strong

So the version with -in is more definite and specific.

Because Icelandic often uses a suffixed definite article. Instead of putting a separate word before the noun, it attaches the article to the noun itself.

So English:

the love

becomes Icelandic:

ástin

This is a very common feature of Icelandic and one of the first things learners notice.

It is capitalized here simply because it is the first word of the sentence.

The noun itself is normally written ástin with a lowercase á unless it begins a sentence or is part of a title.

Also, Á is not just A with decoration. It is a separate Icelandic letter with its own pronunciation.