Learn Icelandic: Ég hef áhuga á tónlist.

In English, we use an adjective and say 'I am interested'. Icelandic uses a noun phrase instead: að hafa áhuga á, which literally translates to 'to have interest in'. So you use the verb að hafa (to have).

Why is the word for interest spelled áhuga instead of its dictionary form áhugi?

Áhugi is a masculine noun. Because it is the direct object of the verb hafa, it takes the accusative case. For weak masculine nouns ending in -i, the ending changes to -a in the accusative, giving us áhuga.

Does the preposition á usually mean 'in'?

Normally, á means 'on', and í means 'in'. However, prepositions often do not map perfectly between languages. The phrase hafa áhuga á is a fixed expression, so you just need to memorize that Icelandic uses á when talking about being interested in something.

What case is tónlist in here?

It is in the dative case, because the preposition á controls the dative case in this specific expression. Tónlist is a feminine noun that does not change its spelling across the nominative, accusative, or dative cases, which is why it looks exactly like the dictionary form here.