Matjurtagarðurinn verður grænni eftir því sem líður á sumarið.

It is a compound noun, which is very common in Icelandic.

• matjurta- = a linking form related to matjurt, meaning a vegetable plant
• garður = garden
• -inn = the suffixed definite article, meaning the

So matjurtagarðurinn means the vegetable garden.

A more literal breakdown is something like the garden of vegetables, but in natural English the vegetable garden is the right meaning.

Here it most naturally means becomes or gets.

The verb verða can sometimes express future meaning, but it also very often means become. In this sentence, because it is followed by a comparative adjective, it describes a change of state:

• verður grænni = gets greener / becomes greener

So the idea is not just that the garden will be green at some later point, but that it is gradually becoming greener.

Because the sentence is comparing one stage with another. The garden is not just green; it is getting greener.

• grænn = green
• grænni = greener

After verða, the adjective is a predicate adjective, and it agrees with matjurtagarðurinn. Since matjurtagarðurinn is masculine singular, grænni is the form used here.

Because not all Icelandic adjectives make the comparative with a simple -ari ending.

Some adjectives have other comparative patterns, and grænn is one of them:

• grænn = green
• grænni = greener
• grænastur = greenest

So grænni is just the correct comparative form you need to learn for this adjective.

As a whole, eftir því sem means as, in proportion as, or the more / as ... goes on.

It should not be translated word for word. Even though the individual words may suggest something like after that which, the expression functions as a fixed phrase.

In this sentence:

• eftir því sem líður á sumarið = as the summer goes on

It comes from the expression líða á, which is used about time passing.

A fairly literal sense is:

• líða á = wear on, advance, go on

So líður á sumarið means the summer wears on or the summer progresses.

In natural English, the best translation here is usually:

• as the summer goes on

Because Icelandic often does not use a dummy subject where English does.

English often says things like:

• it is raining
• it is getting late
• as it gets later in the summer

But Icelandic very often leaves out that kind of empty it. So líður á sumarið is a normal impersonal expression even though there is no separate subject word.

In this expression, líða á takes the time period in the accusative.

So sumarið here is accusative singular definite.

A useful thing to notice is that with a neuter noun like sumar, the nominative and accusative singular look the same, so you cannot see the case difference from the form alone:

• nominative definite: sumarið
• accusative definite: sumarið

Because Icelandic and English do not use the definite article in exactly the same way.

In idiomatic time expressions like líður á sumarið, Icelandic commonly uses the definite form. So even if English might simply say as summer goes on, Icelandic naturally says sumarið here.

So this is something to learn as part of the expression, rather than trying to match English article usage exactly.

Yes, the word order is normal.

The sentence has:

• main clause: Matjurtagarðurinn verður grænni
• subordinate clause: eftir því sem líður á sumarið

You can also put the subordinate clause first:

Eftir því sem líður á sumarið verður matjurtagarðurinn grænni.

That still means the same thing. This is a useful pattern to know, and it also shows Icelandic's usual tendency to keep the finite verb in second position in the main clause.