Learn Icelandic: Innleiðingin mun hafa byrjað þegar við komum. - The implementation will have started when we arrive.

We use the helper verb munu (conjugated here as mun for the third person singular), followed by the infinitive hafa, and then the supine form of the main verb, which here is byrjað. This exactly mirrors the English structure of will have started.

Why is komum in the present tense when our arrival is clearly in the future?

In Icelandic, just like in English, we use the present tense inside time clauses introduced by words like þegar to talk about the future. We say when we arrive rather than when we will arrive, so Icelandic naturally uses þegar við komum.

What exactly is a supine form, as seen in byrjað?

The supine is the specific form of a verb used directly after hafa to create perfect tenses. It looks identical to the neuter singular nominative form of the past participle. For the regular verb byrja, the supine is always byrjað.

What is the root of Innleiðingin and how does its ending work?

The base noun is innleiðing, meaning implementation or introduction. Like almost all nouns ending in -ing, it is a feminine noun. The -in at the end is the attached definite article, shifting the meaning from an implementation to the implementation.