An Undesirable is a criminally-wanted wizard by the Ministry of Magic, similar to a "Public Enemy" or "Most Wanted" in the Muggle world. From 1997-1998, Harry Potter was marked Undesirable No. 1, ostensibly for involvement in the murder of Albus Dumbledore. This made him the most sought-after wizard by the government. The reward for the capture of him and his wand reached 200,000 Galleons in April of 1998.