Australian History By danialasf Apr 29, 1770 Captain Cook claims possession of Australia for the British Crown Jan 26, 1788 First Fleet Arrives May 29, 1788 First Conflict Took place near Rushcutters Bay Sydney and 2 convicts killed Apr 1, 1789 Small Pox Epidemic 1792 Bennelong went to England 1795 Richmond Hill Battle Between Aboriginal people and British People for the country 1803 The black War (Tasmania)