Learn Icelandic: Mig langar að sofa á sófa.

The verb langar (to want) is an impersonal verb. It does not take a normal subject like ég (I). Instead, the person who wants something is forced into the accusative case, which is mig (me). It is almost like saying 'it longs me to sleep'.

Why is the word for sofa spelled sófa here instead of its dictionary form sófi?

This is because of the preposition á (on). In this sentence, á describes a static location where the sleeping happens. When á shows a stationary position rather than movement, the noun following it must be in the dative case. The dative form of the masculine noun sófi is sófa.

Will the preposition á always trigger the dative case like it does here?

Not always! Prepositions like á and í take the dative case when describing a static location (like resting on a sofa). However, if you were describing active movement onto the sofa from somewhere else, á would take the accusative case instead.

What is the purpose of the word að before sofa?