55 Three Levels of Government
Australia is a federation and power is shared between three levels of government. Each level of government is run by a democratically elected council or parliament. These councils and parliaments have power to collect taxes to pay for their own programs although funds are transferred from the Commonwealth to the states, territories and local governments. States also fund local council activities.
The powers of the Commonwealth are listed in section 51 of the Constitution and include defence, foreign affairs, trade and immigration. State powers include almost everything that the states did not give to the Commonwealth when the federation was formed in 1901 and include health, education, transport, agriculture and forests.
Local government powers are defined by Acts of Parliament in each state, and include building regulations, waste management, recreation spaces and dog control.
The three levels share powers over some things such as roads, environmental management and public health.
Download: Fact Sheet 55 - Three Levels of Government [204KB]
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The Australian Constitution - Part V - Powers of the Parliament (Section 51)
http://www.aph.gov.au/senate/general/constitution/par5cha1.htm
More information
Department of Foreign Affairs and Trade: Australia's system of government
http://www.dfat.gov.au/facts/sys_gov.html