Ég vil léttan hádegismat í dag.

Because léttan has to match hádegismat in gender, number, and case.

• hádegismatur = lunch and is masculine singular
• In this sentence, it is the direct object of vil (want), so it goes into the accusative case
• The adjective léttur (light) must match that, so it becomes léttan

So:

• nominative: léttur hádegismatur
• accusative: léttan hádegismat

That is why léttan is used here.

The dictionary form is hádegismatur, but Icelandic nouns change form depending on their case.

Here, hádegismatur is the object of vil, so it is in the accusative:

• nominative: hádegismatur
• accusative: hádegismat

This kind of change is very common in Icelandic masculine nouns.

Icelandic does not have an indefinite article like English a/an.

So léttan hádegismat can mean:

• a light lunch

without needing a separate word for a.

If Icelandic wants to be more specific, it can use other words, but normally the bare noun is enough.

Vil is the 1st person singular present tense of vilja, which means to want.

So:

• ég vil = I want
• þú vilt = you want
• hann/hún vill = he/she wants

It is a common verb, and its present-tense forms are somewhat irregular, so it is worth memorizing.

When vilja has a direct object, that object is normally in the accusative.

In this sentence:

• Ég vil = I want
• léttan hádegismat = the thing being wanted

So both the noun and its adjective appear in the accusative.

This is why you see:

• léttan
• hádegismat

rather than their nominative forms.

Yes. Icelandic very often forms compound words, much more freely than English.

Hádegismatur is made from:

• hádegi = noon / midday
• matur = food / meal

So literally it is something like midday-meal, which English expresses as lunch.

Writing it as one word is completely normal in Icelandic.

Í dag literally means in day, but idiomatically it means today.

It is a fixed everyday expression:

• í dag = today
• á morgun = tomorrow
• í gær = yesterday

Even though English uses a single word, Icelandic uses this two-word phrase.

Yes. Icelandic word order is fairly flexible, especially with time expressions.

You can say:

• Ég vil léttan hádegismat í dag.
• Í dag vil ég léttan hádegismat.

Both are natural. The second version puts more emphasis on today.

The version you have is a very straightforward neutral word order.

Ég vil léttan hádegismat í dag is grammatical and understandable, but depending on context, it can sound a bit direct, like I want.

In everyday speech, Icelandic often uses softer expressions such as:

• Mig langar í léttan hádegismat í dag. = I feel like / I’d like a light lunch today

So:

• ég vil = stronger, more direct
• mig langar í = often more natural for cravings or preferences

Still, your sentence is perfectly correct.

Because the sentence means a light lunch, not the light lunch.

Icelandic often marks definiteness by attaching the article to the noun. For example, the lunch would use a definite form, not the bare noun.

Here the noun is indefinite, so you just get:

• léttan hádegismat

That matches the English meaning a light lunch.

A rough English-friendly guide is:

Yehg vil lyeth-tan HAU-theygh-is-mat ee dowg

A few useful pronunciation notes:

• Ég: the g is soft; the word does not sound like the English name egg
• léttan: tt is pronounced distinctly, and é is a clear long vowel
• hádegis-: the á sounds like ow in cow
• í sounds like ee
• dag has a long a sound, and the final g is not a hard English g

A perfect pronunciation guide depends on dialect and phonetic detail, but this should help you get close.

Yes. That would simply mean:

• I want lunch today

Adding léttan gives extra information:

• Ég vil hádegismat í dag. = I want lunch today.
• Ég vil léttan hádegismat í dag. = I want a light lunch today.

So léttan is just modifying the noun and must agree with it grammatically.

The main dictionary forms are:

• ég = I
• vilja = to want
• léttur = light
• hádegismatur = lunch
• í dag = today

But in actual sentences, Icelandic words often appear in changed forms, such as:

• vil from vilja
• léttan from léttur
• hádegismat from hádegismatur

That is a normal part of Icelandic grammar.