The European Discovery and the Colonisation of Australia is a nice essay on the beginning of European history in Australia. The site was created and is maintained by the Australian government.
From the site:
The first records of European mariners sailing into ‘Australian’ waters occurs around 1606, and includes their observations of the land known as Terra Australis Incognita (unknown southern land). The first ship and crew to chart the Australian coast and meet with Aboriginal people was the Duyfken captained by Dutchman, Willem Janszoon.
Between 1606 and 1770, an estimated 54 European ships from a range of nations made contact. Many of these were merchant ships from the Dutch East Indies Company and included the ships of Abel Tasman. Tasman charted parts of the north, west and south coasts of Australia which was then known as New Holland.