One can visit Amorgos mainly by boat as there is no airport on the island except of a helipad.  Blue Str Ferries is the main transporter, as there is a daily connection from Pireaus port to the island.  Detail schedule one can find at
In addition to the big ferries, there is a daily connection with all small Cyclades by Express Scopelitis, a smaller veseal which has base on Amorgos. There also other companies which facilitate travelers depending on the season. 
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