Fyrirlesarinn byrjaði á stuttri kynningu áður en hún sýndi glærurnar.

It is the noun fyrirlesari + the suffixed definite article -inn.

• fyrirlesari = lecturer, speaker
• fyrirlesarinn = the lecturer

Icelandic usually adds the to the end of the noun instead of using a separate word like English the.

In this sentence, fyrirlesarinn is nominative singular, because it is the subject of the sentence.

This is a very common learner question.

Fyrirlesari is a noun with grammatical masculine gender, but it can still refer to a woman in real life. Icelandic grammatical gender and natural gender are not always the same thing.

So here:

• fyrirlesarinn = the lecturer
• hún = she

That tells you that the lecturer is female, even though the job title itself is grammatically masculine.

Here byrja á is a fixed verb expression meaning to begin with or to start by.

So:

• byrja á einhverju = begin with something

In this sentence:

• byrjaði á stuttri kynningu = started with a short introduction

So á is not being translated literally as on here. It is just the preposition that belongs with this verb pattern.

Because byrja á takes the dative case here.

That means both the adjective and the noun have to be in the dative singular feminine:

• stuttur → stuttri
• kynning → kynningu

So:

• á stuttri kynningu = with a short introduction

A useful way to think about it is:

• nominative: stutt kynning
• dative: stuttri kynningu

The adjective changes to match the noun in gender, number, and case.

Because in the expression byrja á einhverju, the noun after á is normally in the dative.

This is something you often just have to learn together with the verb:

• byrja á kaffinu
• byrja á verkefninu
• byrja á stuttri kynningu

So this is less about the basic spatial meaning of á, and more about the case pattern used by the expression byrja á.

Áður en means before when it introduces a clause.

So:

• áður en hún sýndi glærurnar = before she showed the slides

You can think of it as:

• áður = earlier / before
• en = introducing the following clause

Together they work like the English conjunction before.

Normally, no. Icelandic usually needs an expressed subject in a finite clause.

So:

• hún sýndi glærurnar = she showed the slides

Leaving out hún would usually sound incomplete in a normal sentence.

Unlike some languages, Icelandic is generally not a language where subject pronouns can freely be dropped.

Sýndi is the past tense of the verb sýna = to show.

So:

• sýna = to show
• sýndi = showed

In this sentence both main actions are in the past:

• byrjaði = started
• sýndi = showed

That gives a straightforward past-time sequence: first the introduction, then the slides.

Glærurnar is the definite plural form of glæra.

• glæra = slide
• glærur = slides
• glærurnar = the slides

Here it is the direct object of sýndi, so it is in the accusative plural. For this noun, the definite nominative and accusative plural look the same: glærurnar.

After áður en, you get a subordinate clause, and the word order is more straightforward:

• hún sýndi glærurnar
• subject + verb + object

That is different from Icelandic main-clause verb-second patterns.

So in this sentence:

• main clause: Fyrirlesarinn byrjaði á stuttri kynningu
• subordinate clause: áður en hún sýndi glærurnar

The subordinate clause does not require the same kind of inversion you often see in main clauses.

Most likely yes, especially if this sentence is read by itself.

But grammatically, hún could refer to some other previously mentioned female person if the wider context supported that. Pronouns depend on discourse context, not just grammar.

So in isolation, the normal interpretation is:

• hún = the lecturer

Yes. A more word-for-word version would be something like:

• The lecturer started with a short introduction before she showed the slides.

That is already very close to the Icelandic structure:

• Fyrirlesarinn = the lecturer
• byrjaði á = started with
• stuttri kynningu = a short introduction
• áður en = before
• hún sýndi = she showed
• glærurnar = the slides

So the Icelandic sentence is actually fairly close to natural English in its overall structure.