Abjuration is the solemn repudiation, abandonment, or renunciation by or upon oath, often the renunciation of citizenship or some other right or privilege. (It comes from the Latin abjurare, "to forswear").
Abjuration of the realm 
Abjuration of the realm was a type of abjuration in ancient English law. The person taking the oath swore to leave the country directly and promptly never to return to the kingdom unless by permission of the sovereign. This was often taken by fugitives who had taken sanctuary:
I swear on the Holy Book that I will leave the realm of England and never return without the express permission of my Lord the King or his heirs. I will hasten by the direct road to the port allotted to me and not leave the King's highway under pain of arrest or execution. I will not stay at one place more than one night and will seek diligently for a passage across the sea as soon as I arrive, delaying only one tide if possible. If I cannot secure such passage, I will walk into the sea up to my knees every day as a token of my desire to cross. And if I fail in all this, then peril shall be my lot.
English Commonwealth 
Near the start of the English Civil War, on 18 August 1643 Parliament passed "An Ordinance for Explanation of a former Ordinance for Sequestration of Delinquents Estates with some Enlargements." The enlargements included an oath which became known as the "Oath of Abjuration":
I ..; Do abjure and renounce the Pope's Supremacy and Authority over the Catholic Church in General, and over my self in Particular; And I do believe that there is not any Transubstantiation in the Sacrament of the Lords Supper, or in the Elements of Bread and Wine after Consecration thereof, by any Person whatsoever; And I do also believe, that there is not any Purgatory, Or that the consecrated Host, Crucifixes, or Images, ought to be worshipped, or that any worship is due unto any of them; And I also believe that Salvation cannot be Merited by Works, and all Doctrines in affirmation of the said Points; I do abjure and renounce, without any Equivocation, Mental Reservation, or secret Evasion whatsoever, taking the words by me spoken, according to the common and usual meaning of them. So help me God.
In 1656, it was reissued in what was for Catholics an even more objectionable form. Everyone was to be "adjudged a Papist" who refused this oath, and the consequent penalties began with the confiscation of two thirds of the recusant's goods, and went on to deprive him of almost every civic right.
The Catholic Encyclopaedia make the point that the oath and the penalties were so severe that it stopped the efforts of the Gallicanizing party among the English Catholics, who had been ready to offer forms of submission similar to the old oath of Allegiance, which was condemned anew about this time by Pope Innocent X.
Great Britain and Ireland 
In England (and after 1707 Great Britain) the Oath of Abjuration denied the royal title of James II's heirs (i.e. the direct Catholic descendent of the House of Stuart exiled after the Glorious Revolution in 1688). In England, an Oath of Abjuration was taken by Members of Parliament, clergy, and laymen, pledging to support the current British monarch and repudiated the right of the Stuarts and other claimants to the throne. This oath was imposed under William III, George I and George III. It was superseded by the oath of allegiance. In Ireland the oath was imposed of state office holders, teachers and lawyers, and on clergy of the established church in from 1703, the following year it was on all Irish voters and from 1709 it could be demanded of any adult male by a magistrate.
The Netherlands 
Another famous abjuration was brought about by the Plakkaat van Verlatinghe of July 26, 1581, the formal Declaration of Independence of the Low Countries from the Spanish king, Philip II. This oath was the climax of the Eighty Years' War (Dutch Revolt).
- C.H. Firth, R.S. Rait (editors (1911)). Acts and Ordinances of the Interregnum, 1642-1660, "August 1643: An Ordinance for Explanation of a former Ordinance for Sequestration of Delinquents Estates with some Enlargements", pp. 254-260. Date accessed: 16 March 2010
- One or more of the preceding sentences incorporates text from a publication now in the public domain: Herbermann, Charles, ed. (1913). "English Post-Reformation Oaths". Catholic Encyclopedia. Robert Appleton Company.
- "English Post-Reformation Oaths". Catholic Encyclopedia. New York: Robert Appleton Company. 1913. Cites Reusch, Index der verboten Bücher (Bonn, 1883)