Ef ég sé villu í textanum, skrifa ég athugasemd við textann.

Sjá is the infinitive, meaning to see. After ég you need the 1st person singular present tense form, which is sé.

So:

• að sjá = to see
• ég sé = I see
• þú sérð = you see
• hann/hún/það sér = he/she/it sees

This verb is irregular, so the form does not look very similar to the infinitive.

Because villu is the accusative singular form of villa.

Here, villa is the direct object of sé:

• Ég sé villu = I see an error

The noun villa is a feminine noun, and in the singular it changes like this:

• nominative: villa
• accusative: villu
• dative: villu
• genitive: villu

So in this sentence, Icelandic uses the accusative because the error is what is being seen.

Because the same noun is being used in two different grammatical cases.

The basic noun is texti = text. In the sentence it appears in the definite form twice:

• í textanum
• við textann

These are different because the prepositions require different cases.

1. í textanum

Here í means in, with no movement involved, so it takes the dative:

• í textanum = in the text

2. við textann

Here við takes the accusative in this expression:

• við textann = on/about the text

So the endings are different because Icelandic marks the noun’s role much more clearly than English does.

Because í can take either the dative or the accusative, depending on meaning.

• dative = location, being inside something
• accusative = movement into something

In this sentence, the meaning is location: the error is in the text, not moving into it. So Icelandic uses the dative:

• í textanum = in the text

Compare:

• Ég sé villu í textanum = I see an error in the text
• Ég set orðið í textann = I put the word into the text

That location vs. motion distinction is very common in Icelandic.

Yes, við often has meanings like with, by, or against, but prepositions in Icelandic are often idiomatic. You cannot always translate them word-for-word.

In the expression:

• athugasemd við e-ð

the preposition við means something like:

• comment on
• remark about

So:

• skrifa athugasemd við textann = write a comment on/about the text

This is just the normal Icelandic phrasing. It is best learned as a set expression.

Good question. Athugasemd is also a direct object here, but its nominative and accusative singular forms are the same.

So even though it is functioning like villu grammatically, its form does not visibly change.

That is very common in Icelandic: some nouns show a clear case ending change, and some do not.

So here:

• skrifa athugasemd = write a comment

Even though it is accusative, it looks the same as the dictionary form.

Because Icelandic follows a verb-second pattern in main clauses.

The sentence starts with the subordinate if-clause:

• Ef ég sé villu í textanum

After that, the main clause begins. Since the first slot of the sentence is already occupied by the if-clause, the finite verb of the main clause comes next:

• skrifa ég athugasemd við textann

So the pattern is:

• first element: Ef ég sé villu í textanum
• second position: skrifa
• then subject: ég

If you wrote the main clause by itself, it would normally be:

• Ég skrifa athugasemd við textann

But after an initial clause like Ef..., inversion happens.

It can often be understood as a general condition, and that is probably the most natural reading here:

• If I see an error in the text, I write a comment on the text

That sounds like a habitual or regular action.

But Icelandic, like English, can also use the present tense in conditional sentences for future meaning, depending on context. So it could also mean something close to:

• If I see an error in the text, I’ll write a comment

The exact meaning depends on the situation. The grammar itself is completely normal for this kind of sentence.

Because the first part of the sentence is a subordinate clause introduced by ef:

• Ef ég sé villu í textanum

In Icelandic, it is standard to separate that kind of introductory subordinate clause from the main clause with a comma:

• Ef ..., skrifa ég ...

So the comma marks the boundary between:

1. the if-clause
2. the main clause

This is very common in written Icelandic.

Ef means if and introduces a conditional clause.

So:

• Ef ég sé villu í textanum = If I see an error in the text

It sets up the condition for what happens in the main clause:

• skrifa ég athugasemd við textann = I write a comment on the text

So the whole sentence has the structure:

• If X happens, Y happens

That is one of the most basic and common uses of ef in Icelandic.