Hann sver að segja sannleikann.

Here að is the infinitive marker, so it works like English to in to tell.

• að segja = to say / to tell
• Hann sver að segja sannleikann = He swears to tell the truth

This is not the conjunction að meaning that. In this sentence, it introduces an infinitive verb.

Because segja is in the infinitive form.

After the infinitive marker að, Icelandic normally uses the infinitive:

• að segja = to tell
• segir = tells / is saying (finite, present tense)

So:

• hann segir = he says
• hann sver að segja = he swears to say / tell

Just like in English, He swears to tell..., not He swears tells...

Because sver is the present-tense form that agrees with hann.

The verb is sverja = to swear.
Its present forms include:

• ég sver = I swear
• þú sverð = you swear
• hann sver = he swears

So sverja is the dictionary form, while sver is the correctly conjugated form for he.

Because sannleikann is the definite accusative singular of sannleikur.

Breakdown:

• sannleikur = truth (dictionary form, nominative singular)
• sannleikann = the truth (accusative singular, definite)

It has this form because it is the direct object of segja:

• segja sannleikann = tell the truth

This is a very common Icelandic pattern: the noun changes form depending on its role in the sentence.

In Icelandic, the definite article is usually attached to the end of the noun rather than written as a separate word like English the.

So instead of a separate word, Icelandic often does this:

• sannleikur = truth
• sannleikurinn = the truth (subject form)
• sannleikann = the truth (object form)

That attached ending is one of the normal features of Icelandic grammar.

Yes. The understood subject of að segja is also hann.

So the sentence means:

• He swears [that he will] tell the truth
• or more literally, He swears to tell the truth

This works much like English. In He promises to come, the person who promises is also the person who comes. Icelandic does the same kind of thing here.

Yes, að can also mean that as a conjunction, but here it means to because it is followed by an infinitive:

• að segja = to tell

A useful clue is the verb form after it:

• að segja → infinitive → to
• að hann kemur → full clause with subject + finite verb → that

So in this sentence, since segja is infinitive, að is the infinitive marker.

Yes, it is a very common expression meaning to tell the truth.

It is similar to the English expression and is used naturally in Icelandic. Learners may also come across segja satt, which means something like say what is true / tell the truth, but segja sannleikann is a very straightforward and common way to express the idea.

It is grammatical and natural, but sverja gives the sentence a fairly strong or solemn tone.

So Hann sver að segja sannleikann sounds like:

• he swears an oath
• he solemnly swears
• he strongly promises

In everyday speech, a weaker verb like lofa (promise) might be more common in some contexts. But this sentence is perfectly natural when the idea of swearing is important.

The structure is:

• Hann = subject
• sver = finite verb
• að segja sannleikann = infinitive phrase

So the pattern is:

Subject + verb + infinitive phrase

That is very similar to English:

• He swears to tell the truth

Nothing unusual is happening with the word order here; it is a straightforward main clause.