Act of Supremacy 1558

The Act of Supremacy 1558 (1 Eliz 1 c 1), sometimes referred to as the Act of Supremacy 1559, is an act of the Parliament of England, passed under the auspices of Elizabeth I. It replaced the original Act of Supremacy 1534 issued by Elizabeth's father, Henry VIII, which arrogated ecclesiastical authority to the monarchy, and which had been repealed by Mary I. Along with the Act of Uniformity 1558 it made up what is generally referred to as the Elizabethan Religious Settlement.
The act remained in place until the 19th century, when some sections began to be repealed. By 1969 all save section 8 had been repealed by various acts. The whole Act was repealed in Northern Ireland in 1950 and 1953. Section 8 is still in force in Great Britain .
Act of 1559.
The act revived 10 acts which Mary I had reverted, significantly clarified and narrowed the definition of what constituted heresy, and confirmed Elizabeth as Supreme Governor of the Church of England. Supreme Governor was a suitably equivocal title that made Elizabeth head of the Church without ever saying she was. This was important because many felt that a woman could not rule the church. 
The act also made it a crime to assert the authority of any foreign prince, prelate, or other authority, and was aimed at abolishing the authority of the Pope in England. A third offence was high treason, punishable by death.
Oath of Supremacy.
The Oath of Supremacy, imposed by the Act of Supremacy 1558, provided for any person taking public or church office in England to swear allegiance to the monarch as Supreme Governor of the Church of England. Failure to so swear was a crime, although it did not become treason until 1562, when the Supremacy of the Crown Act 1562 made refusal to take the oath a treasonable offence. The Oath was later extended to include Members of Parliament and people studying at universities: all but one of the bishops lost their posts and a hundred fellows of Oxford colleges were deprived, as many dignitaries resigned rather than take the oath. The bishops who were removed from the ecclesiastical bench were replaced by appointees who would agree to the reforms. 
Text of the oath as published in 1559:
This had a specific impact on English Roman Catholics since it expressly indicates that they must forswear allegiance to Roman Catholicism, inasmuch as the Church of Rome was directly a foreign jurisdiction, power, superiority and authority. However, during the early years of her reign Elizabeth practiced religious clemency and tolerance, which was an attempt to harmonise the state of affairs between the Roman Catholics and the Church of England. This was necessary for Elizabeth to fully establish her power, hold off threats of invasion from France and Spain, and to counter accusations of illegitimacy that plagued her early years. In the last twenty years of her reign, as the Pope issued official encouragement to topple, and even kill, Elizabeth, as Jesuits infiltrated England, and as the threat of Spanish invasion loomed, Catholics became targets for oppression. Later, Roman Catholic power within England waned (because Roman Catholics were forbidden to take public office and were slowly deprived of their lands and fortunes) but their influence grew until they attempted the Gunpowder Plot in 1605 – whereupon they were oppressed for nearly 200 years.
Text in force today.
Section 8 still remains in force in Great Britain, and reads as follows:
Related legislation.
An act to the same effect was passed in Ireland in the following year, the Act of Supremacy (Ireland) 1560 (2 Eliz.1 c. 1).
The Papal Jurisdiction Act 1560 remains in force in Scotland.
Another act (1 Eliz.1 c.5) dealing with treason was passed in 1558, which made it treason to "compass" or "imagine" to deprive the Queen (or her heirs) of the Crown, or destroy her or her heirs, or levy war against them in their dominions, or depose them, or say that they are not or ought not to be the monarch.
Another act (1 Eliz.1 c.6) dealt with sedition.