Hi Toqual,
Trespass is both a criminal and civil (private) offence. In short, you can be sued by an individual (usually the owner) and the state/police.
Trespass is an offence against property, meaning that you have interfered with the rights of the owner or rightful possessor without their permission.
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Inclosed Lands Protection Act 1901 (NSW) sections 4 and 4A: it is an offence to enter into enclosed lands without a lawful excuse and without the owner's permission
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Crimes Act 1914 (Cth) section 89: it is an offence to trespass onto commonwealth land
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Public Order Act 1971 (Cth) section 11 and 12: it is an offence to enter into or obstruct commonwealth or territory property
If you trespass into restricted private land, you may be committing a civil tort, in addition to one of the criminal offences above, as well as breaching a contractual term (e.g. where you purchase a ticket to enter into a transport area and there are terms attached to that ticket).