Lieutenant James Cook charts Australia’s eastern coastline and proclaims it Britain’s possession. This marks the first claim to British sovereignty over the Australian continent. It follows the issue by the British Government of the Secret Instructions for Lieutenant James Cook Appointed to Command His Majesty’s Bark the Endeavour 30 July 1768. Cook made three voyages to the South Pacific between 1768 and 1779.

In July 1776, the 13 American colonies declare independence from Great Britain and establish the United States of America. The revolutionaries are inspired by republican ideals of equality, liberty and people's right to govern themselves. A peace treaty in 1783 ends the war with Britain and recognises the sovereignty of the United States.

The British Government selects Captain Arthur Phillip to establish a new British colony, to become known as New South Wales. His first Commission is signed on 12 October 1786. A second Commission issued in April 1787 appoints Captain Phillip as Captain-General and Commander-in-Chief of the First Fleet, and a third Commission, dated 24 April 1787, provides him with details concerning the limits of the new colony and sets out his general tasks.

The New South Wales Courts Act 1787 (UK) establishes the first criminal court in Australia to impose discipline in the new penal colony.

Australia’s first Charter of Justice is issued by the British Parliament. This provides the authority for the establishment of the first NSW Courts of Criminal and Civil Jurisdiction, and establishes a Deputy Judge-Advocate, a Civil Court and six court officers to be appointed by the Governor. The Governor is required to give his permission for any death sentence imposed by the Court, and is empowered to give pardons. The Civil Court has the power to deal with disputes over property and has jurisdiction over wills and estates. A Second Charter established in 1814 creates the three Courts of Civil Judicature: Governor’s Court, Supreme Court and Lieutenant Governor’s Court.

A printing press arrives with the First Fleet. It is another eight years before a convict with skills to work the press can be found, but it plays a important role in disseminating ideas, waging political campaigns, and promoting public debate and awareness of issues; crucial issues in the history of Australian democracy. George Hughes, Australia's first government printer, produces over 200 individual government orders and regulations between 1796 and 1800. He also prints playbills for the first two plays staged in the colony: Farquhar. The Recruiting Officer and Shakespeare. Henry the Fourth. Hughes is replaced by another convict, George Howe, and in 1802 he publishes the colony's first book, "New South Wales Standing Orders". In 1803, he publishes the first newspaper, The Sydney Gazette and New South Wales Advertiser and, 16 years later, the first literary work, "First Fruits of Australian Poetry" by Judge Barron Field.

On 19 January the First Fleet enters Botany Bay under the command of Captain Arthur Phillip, and on 26 January, from the landing site at Port Jackson in Sydney Cove, he proclaims the new colony of New South Wales. The First Fleet comprises 1030 people including male and female convicts, marines and civil officers and their wives, and 37 children.

Governor Phillip assembles Australia’s first Court of Criminal Jurisdiction, and Samuel Barsby is the first person to be brought before Judge-Advocate David Collins and the six officers of the Court. Barbsy is found guilty of personally abusing a drum major in the Detachment of Marines and of striking a drummer with an adze. He is sentenced to receive 150 lashes with a cat-o’-nine-tails.

The arrival of the First Fleet in January 1788 signals the beginning of British colonisation in Australia. Convicts and soliders establish a settlement on the southern shores of Sydney Harbour, the traditional territory of the Indigenous Eora people, and the British Government issues instructions to the colonial Governor to treat the Indigenous inhabitants kindly. However, it does not recognise Indigenous ownership of the land, nor are the Indigenous inhabitants protected by law as they are not considered to be British subjects. Conflict erupts on the colonisal 'frontier', as white settlement escalates and Indigenous inhabitants resist colonisation and defend their territory and resources. Thousands of Indigenous people are killed in the process, leading to calls by the 1830s and 1840s for greater protection of Indigenous people and the establishment of Indigneous reserves and protection boards.

In the first civil court action in Australia, convicts Henry Cable and his wife successfully sue the captain of their transportation vessel over a lost parcel. Cable later becomes a merchant in New South Wales.

The French people rise up against absolute monarchism and the feudal privileges of the aristocrats and Catholic clergy during a time of famine, unemployment and a national financial crisis. The revolution's leaders support Enlightenment ideals of reason, liberty, equality and fraternity.

The Polish Constitution of 3 May under King Stanislaw August is Europe's first democratic codified constitution creating a constitutional monarchy. It introduces political equality between townsfolk and nobility, and places peasants under government protection. It is influenced by the British and American experience.

The Haitian Revolution — the world's first successful slave revolt — establishes a free republic in the French colony under the leadership of former slave, Toussaint Louverture.

Thomas Muir, Thomas Palmer, William Skirving and Maurice Margarot are sentenced to transportation to New South Wales for their part in advocating parliamentary and constitutional reform in Britain. Their radical ideas are influenced by the French Revolution and, together with Joseph Gerrald who was transported later, they become known as the Scottish Martyrs.

NSW Governor Philip King establishes Australia's first welfare institution — a girls' Orphan School. The first private welfare organisation — the Benevolent Society of New South Wales — forms on 8 May 1813 to aid the poor.

Colonel David Collins chooses the site of Hobart as the base for the new convict settlement of Van Diemen’s Land, and serves as Lieutenant-Governor until his death in 1810.

One of Australia’s first convict uprisings occurs at Castle Hill in New South Wales when predominantly Irish Catholic convicts attempt to escape from servitude. After clashing with government troops the rebel leader, Philip Cunningham, is captured and hanged.

Britain outlaws the slave trade in the British Empire, although it is still legal to own slaves. The complete abolition of slavery in Britain and its colonies does not occur until 1833.

Tensions over power in the new colony erupt when Governor William Bligh arrests John Macarthur, a prominent pastoralist, and refuses him the bail granted by an illegally constituted court. The commander of the NSW Corps, Major George Johnston, deposes Bligh and assumes government of the colony. Macarthur serves as colonial secretary until Bligh is replaced by Lieutenant-Colonel Foveaux. Johnston is later dismissed for his part in the mutiny, while Macarthur is exiled from the colony for seven years.

Matthew Flinders completes the first circumnavigation of the continent in 1803. He writes in his journal, A Voyage to Terra Australis, that the name Australia is more agreeable to the ear. Governor Macquarie subsequently adopts the name Australia; in official correspondence after receiving a copy of Flinders journal, A Voyage to Terra Australia, published in 1814.

The defeat of France gives Britain about a century of largely unchallenged dominance as an imperial power.

Colonists inherit the Westminster tradition of petitioning the House of Commons. One of Australia’s earliest petitions to the Prince Regent concerns civil and commercial limitations in the colonies, and the lack of an effective legal system. The petition marks the emergence of the Emancipists as a political force in the colonies.

On 16 August a crowd of 60,000 assembles on St Peter's Field in Manchester, England, to demand parliamentary representation for the city. 'Rotten boroughs', like Old Sarum with only 11 voters, had two Members of Parliament whereas Manchester, with 200,000 people, had none. Troops violently attempt to arrest the main speaker. Eleven people are killed and 500 injured.

The Emancipists successfully petition King George IV following an 1817 King’s Bench ruling that people freed by governor’s pardon, unlike those freed by pardons issued under the Great Seal in London, cannot pursue legal action or own property. The ruling is overturned by the New South Wales Act 1823 (UK).

The Charter of Justice 13 October 1823 (UK) establishes a system of justice for Van Diemen's Land and provides for the appointment of John Lewes Pedder to preside over it as Chief Justice. The New South Wales Act 1823 (UK) authorises the establishment of a legislative council in New South Wales and Australia's first supreme courts in New South Wales and Van Diemen's Land, as well as providing for Van Diemen's Land to become a separate colony. The Legislative Council conducts its first meeting in August 1824. These new laws follow criticisms of the administration and justice system in New South Wales and Van Diemen's Land by Commissioner John Thomas Bigge.

The Australian newspaper (no relation to the modern day broadsheet of the same name) begins publication, founded by Dr Robert Wardell and William Wentworth. The colonial press is less restricted than in Britain, and newspapers flourish in the colonies. By 1882 there are 146 newspapers in Victoria, 95 in New South Wales, 47 in South Australia, 27 in Queensland, 11 in Tasmania, and four in Western Australia.

An Order-in-Council separates Van Diemen’s Land from New South Wales following petitions from colonists, and legislative and executive councils are established.

The Mechanics Institute and School of Arts is founded in Hobart and is one of Australia's first public education institutions.

Under the Servants and Labourers Act of NSW servants can be docked wages or imprisoned for refusing to work or for property destruction. Masters found abusing their servants are liable to pay damages. There is considerable debate in the colonies about these laws.

The Australian Courts Act 1828 (UK) ensures that the laws of England will be applied in the two existing Australian colonies: New South Wales and Van Diemen’s Land. The Act strengthens the role of both supreme courts, as appeals from supreme court decisions to the Governor are ended. It provides for trial by jury in the Supreme Court in civil cases and empowers the Governor to introduce general trial by jury in criminal matters. Australian statute law thus has a firm foundation, but is able to evolve according to its own conditions and needs. Trial by jury for people charged under criminal law is established in 1833 in New South Wales and, in limited circumstances, in 1834 in Van Diemen’s Land.