What is Methodism?
Unlike other Christian denominations, Methodism did not arise as a result of doctrinal dispute, but out of an emphasis on practical Christianity. "The underlying energy of the Wesleyan theological heritage stems from an emphasis upon practical divinity, the implementation of genuine Christianity in the lives of believers." 
The founder of the Methodist movement is John Wesley. Wesley was a minister of the Church of England who struggled with his own faith until having an evangelical experience of conversion at Aldersgate. John Wesley himself described the general perception of the newly-formed Methodist group:
The one charge then advanced against them was, that they were "righteous overmuch;" that they were abundantly too scrupulous, and too strict, carrying things to great extremes: In particular, that they laid too much stress upon the Rubrics and Canons of the Church; that they insisted too much on observing the Statutes of the University; and that they took the Scriptures in too strict and literal a sense; so that if they were right, few indeed would be saved. 
History of Methodism
Anglicanism or Episcopalianism is the general form of doctrine, worship and structure based on the tradition of the Church of England, which extends beyond membership in the Anglican Communion.
Anglicanism is characterized by a via media (middle way) between Roman Catholicism and Protestantism. Anglicans are not subject to the Pope and are Protestant in most areas of doctrine, but Anglicans also retain many Catholic forms of worship, including a hierarchy based on bishops (which is the meaning of the world "Episcopalian").
John Wesley (1703 – 1791) was an Anglican cleric and Christian theologian. Wesley is largely credited, along with his brother Charles Wesley, with founding the Methodist movement which began when he took to open-air preaching in a similar manner to George Whitefield.
In contrast to George Whitefield's Calvinism, Wesley embraced the Arminian doctrines that were dominant in the 18th-century Church of England. Methodism in both forms was a highly successful evangelical movement in the United Kingdom, which encouraged people to experience Jesus Christ personally.
Wesley's teachings, known as Wesleyanism, provided the seeds for the modern Methodist movement, the Holiness movement, Pentecostalism, the Charismatic Movement, and Neo-charismatic churches, which encompass numerous denominations across the world.
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