No single country mapped the entire coast of Australia.
The Portuguese were believed to be the first explorers to sight Western Australia, but all records of their journey have been lost. The Dutch did extensive exploration and charting of much of the western coast, but the French also had input into the southern corner. The Dutch, the French and the English all made forays into various parts of Tasmania.
The first to chart the eastern coast was Captain James Cook of England, and he named many features along the coast, but did not explore every bay and inlet.
Between December 1801 and June 1803, Matthew Flinders, also English, charted the entire coastline of Australia. During this time, he filled in some of the information Cook had missed. John Oxley and George Bass were more Englishmen who added to the knowledge of Australia's coastline
Captain Cook and Captain Vancouver
The east coast of Australia was first explored by Captain James cook in 1770.
Spain, he was a Spanish explorer who mapped the Gulf Coast.
Abel Tasman mapped the southern coast of Tasmania which, at the time, he named Van Diemen's land. He did not realise Tasmania was an island.
Captain Cook's first journey to the eastern coast of Australia was in 1770. He charted and explored along the coast between April and August of that year, naming it New South Wales.
No single person mapped the entire west coast of Australia, so it was mapped over many years. The first person to land on Western Australia's coast was Dirk Hartog, in 1616. Between then and 1699, which was William Dampier's second expedition to western Australia, various sections were mapped. Matthew Flinders filled in the gaps when he circumnavigated Australia in 1801-1802.
He mapped the north coast of Australia.
Captain Cook and Captain Vancouver
Portugal explored the coast of west africa
The east coast of Australia was first explored by Captain James cook in 1770.
Spain, he was a Spanish explorer who mapped the Gulf Coast.
Well, he found America! He also mapped/explored the east coast of South America.
Abel Tasman
The east coast of Canada.
William Dampier was an English pirate who first landed on Western Australia's northwest coast in 1688.
England
He explored Tasmania, Australia's north coast and New Zealand.