Mathraki is one of the three Diapontian islands, connected to Corfu by a small ferry (1.5 hours, port of Plakes) that also stops at Ereikoussa and Othoni. The ferry can carry only 5–6 cars and tickets must be purchased on board (no advance booking). The island can also be reached from Aghios Stefanos near Corfu (30 minutes, Aspiotis Lines) or from Sidari. For schedules, see gtp.gr.
To reach Mathraki, first get to Corfu, which has an international airport with direct flights from many European cities in summer and year-round connections from Athens.
Sea connections are more frequent during the summer season (the island is nearly uninhabited in winter); always check availability if travelling in other periods.