Answering the question of What is the Anglican Faith is, my opinion, best started with the Chicago-Lambeth Quadrilateral of 1888.
The Quadrilateral comes from a four-point statement that eventually became a resolution of the Third Lambeth Conference, which was held in 1888. Developed originally by William Reed Huntingdon, a priest in the Protestant Episcopal Church in the United States (ECUSA), as a way to summarize Anglican beliefs in a way that could lead to reunion with Roman Catholics and Eastern Orthodox Christians.
The ECUSA House of Bishops adopted a statement in Chicago in 1886 that partially aligned with Huntingdon’s essay. Two years later at the Third Lambeth Conference a resolution was passed that was closer to his original thesis. The Resolution is as follows:
That, in the opinion of this Conference, the following Articles supply a basis on which approach may be by God’s blessing made towards Home Reunion:
The Holy Scriptures of the Old and New Testaments, as “containing all things necessary to salvation,” and as being the rule and ultimate standard of faith.
The Apostles’ Creed, as the Baptismal Symbol; and the Nicene Creed, as the sufficient statement of the Christian faith.
The two Sacraments ordained by Christ Himself—Baptism and the Supper of the Lord—ministered with unfailing use of Christ’s words of Institution, and of the elements ordained by Him.
The Historic Episcopate, locally adapted in the methods of its administration to the varying needs of the nations and peoples called of God into the Unity of His Church.
The Quadrilateral directly builds on the Thirty-Nine Articles of Religion for the first three statements, while being an extension for the fourth statement. The principal of this has been used in Ecumenical dialogue between Anglicans and non-Anglicans, as well as being used in agreements of Full Communion with the Old Catholic Union of Utrecht, and a number of Lutheran Churches that have either maintained the Episcopate or have re-established it.