Cyrillic Where It Matters: Reading the Signs You Actually Need
Serbia uses both alphabets, and the split is not random. Learn the thirty letters in an evening, then the forty words that appear on the signs you need.
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Cyrillic
How Much Serbian You Actually Need, by Situation
Does Serbia speak English? In a cafe, yes. At a MUP counter, no. The amount of Serbian you need depends entirely on which room you are standing in.
Serbian That Gets a Counter to Help You: Twenty Sentences
You do not need to learn Serbian to get through a Belgrade counter. You need twenty sentences, in the order the window asks for them.