Fjallið er hátt og bókasafnið er undir því.

The mountain is high and the library is under it.

Breakdown of Fjallið er hátt og bókasafnið er undir því.

• vera: to be
• og: and
• undir: under
• bókasafnið: the library

Questions & Answers about Fjallið er hátt og bókasafnið er undir því.

Why does fjallið end with -ið?

fjallið is the definite form of the neuter noun fjall (“mountain”). In Icelandic you don’t use a separate word for “the” – you add a suffix to the noun. For neuter nouns that suffix is -ið, so:
• fjall → fjallið = “the mountain”

Why is the adjective hátt and not something like háttur or hár?

Icelandic adjectives agree in gender, number and case with the noun they describe. The base (dictionary) form is masculine nominative (hár), but here it describes a neuter noun (fjall) and is used predicatively after er. Predicative adjectives take the nominative case, and for neuter singular that means adding -t:
• hár (masc) → hátt (neut. sing. nom.)

Why is there an -s- in bókasafnið?

bókasafnið is a compound noun made from bók (“book”) + safn (“collection” or “repository”). Icelandic often inserts a linking -s- (a genitive element) between the parts:
• bók + safn → bókasafn
Then you add -ið to make it definite:
• bókasafn → bókasafnið = “the library”

What case does undir take in this sentence?

undir can govern either accusative (motion toward) or dative (static location). Here it expresses location (“under”), so it takes the dative case.