As discussed in other threads, we Anglicans don't have definitive confessions of faith or such, and our autocephalic structure means that each national church has their own write-up of what they do want to say by way of definition of beliefs. That said, the 1979 (U.S.) Episcopal Church "An Outline of the Faith, Commonly Called the Catechism" is probably as good a job of defining Anglican beliefs as one can readily find. Here's a link to the online Book of Common Prayer section containing it: http://www.holycross-raleigh.org/bcp/845.html In response to the recommendation by Paladin Valer and BAChristian, I am going to post the contents here. Others (and comments from British, New Zealand, and Australian Anglicans and our REC member(s) will be welcome) can supplement this with doctrinal statements they're more familiar with.
The following posts will give it in full, in the sections into which it is divided.
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"It is written, 'My house shall be a house of prayer,' but you have made it a den of thieves." -Jesus
A We are part of God's creation, made in the image of God.
Q What does it mean to be created in the image of God?
A It means that we are free to make choices: to love, to create, to reason, and to live in harmony with creation and with God.
Q Why then do we live apart from God and out of harmony with creation?
A From the beginning, human beings have misused their freedom and made wrong choices.
Q Why do we not use our freedom as we should?
A Because we rebel against God, and we put ourselves in the place of God.
Q What help is there for us?
A Our help is in God.
Q How did God first help us?
A God first helped us by revealing himself and his will, through nature and history, through many seers and saints, and especially the prophets of Israel.
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"It is written, 'My house shall be a house of prayer,' but you have made it a den of thieves." -Jesus
A The Ten Commandments are the laws give to Moses and the people of Israel.
Q What do we learn from these commandments?
A We learn two things: our duty to God, and our duty to our neighbors.
Q What is our duty to God?
A Our duty is to believe and trust in God;
I To love and obey God and to bring others to know him;
II To put nothing in the place of God;
III To show God respect in thought, word, and deed;
IV And to set aside regular times for worship, prayer, and the study of God's ways.
Q What is our duty to our neighbors?
A Our duty to our neighbors is to love them as ourselves, and to do to other people as we wish them to do to us;
V To love, honor, and help our parents and family; to honor those in authority, and to meet their just demands;
VI To show respect for the life God has given us; to work and pray for peace; to bear no malice, prejudice, or hatred in our hearts; and to be kind to all the creatures of God;
VII To use our bodily desires as God intended;
VIII To be honest and fair in our dealings; to seek justice, freedom, and the necessities of life for all people; and to use our talents and possessions as ones who must answer for them to God;
IX To speak the truth, and not to mislead others by our silence;
X To resist temptations to envy, greed, and jealousy; to rejoice in other people's gifts and graces; and to do our duty for the love of God, who has called us into fellowship with him.
Q What is the purpose of the Ten Commandments?
A The Ten Commandments were given to define our relationship with God and our neighbors.
Q Since we do not fully obey them, are they useful at all?
A Since we do not filly obey them, we see more clearly our sin and our need for redemption.
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"It is written, 'My house shall be a house of prayer,' but you have made it a den of thieves." -Jesus
A Sin is the seeking of our own will instead of the will of God, thus distorting our relationship with God, with other people, and with all creation.
Q How does sin have power over us?
A Sin has power over us because we lose our liberty when our relationship with God is distorted.
Q What is redemption?
A Redemption is the act of God which sets us free from the power of evil, sin, and death.
Q How did God prepare us for redemption?
A God sent the prophets to call us back to himself, to show us our need for redemption, and to announce the coming of the Messiah.
Q What is meant by the Messiah?
A The Messiah is one sent by God to free us from the power of sin, so that with the help of God we may live in harmony with God, within ourselves, with our neighbors, and with all creation.
Q Who do we believe is the Messiah?
A The Messiah, or Christ, is Jesus of Nazareth, the only Son of God.
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"It is written, 'My house shall be a house of prayer,' but you have made it a den of thieves." -Jesus
Q What do we mean when we say that Jesus is the only Son of God?
A We mean that Jesus is the only perfect image of the Father, and shows us the nature of God.
Q What is the nature of God revealed in Jesus?
A God is love.
Q What do we mean when we say that Jesus was conceived by the power of the Holy Spirit and became incarnate from the Virgin Mary?
A We mean that by God's own act, his divine Son received our human nature from the Virgin Mary, his mother.
Q Why did he take our human nature?
A The divine Son became human, so that in him human beings might be adopted as children of God, and be made heirs of God's kingdom.
Q What is the great importance of Jesus' suffering and death?
A By his obedience, even to suffering and death, Jesus made the offering which we could not make; in him we are freed from the power of sin and reconciled to God.
Q What is the significance of Jesus' resurrection?
A By his resurrection, Jesus overcame death and opened for us the way of eternal life.
Q What do we mean when we say that he descended to the dead?
A We mean that he went to the departed and offered them also the benefits of redemption.
Q What do we mean when we say that he ascended into heaven and is seated at the right hand of the Father?
A We mean that Jesus took our human nature into heaven where he now reigns with the Father and intercedes for us.
Q How can we share in his victory over sin, suffering, and death?
A We share in his victory when we are baptized into the New Covenant and become living members of Christ.
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"It is written, 'My house shall be a house of prayer,' but you have made it a den of thieves." -Jesus
A The New Covenant is the new relationship with God given by Jesus Christ, the Messiah, to the apostles; and, through them, to all who believe in him.
Q What did the Messiah promise in the New Covenant?
A Christ promised to bring us into the kingdom of God and give life in all its fullness.
Q What response did Christ require?
A Christ commanded us to believe in him and to keep his commandments.
Q What are the commandments taught by Christ?
A Christ taught us the Summary of the Law and gave us the New Commandment.
Q What is the Summary of the Law?
A You shall love the Lord your God with all your heart, with all your soul, and with all your mind. This is the first and great commandment. And the second is like it: You shall love your neighbor as yourself.
Q What is the New Commandment?
A The New Commandment is that we love one another as Christ loved us.
Q Where may we find what Christians believe about Christ?
A What Christians believe about Christ is found in the Scriptures and summed up in the creeds.
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"It is written, 'My house shall be a house of prayer,' but you have made it a den of thieves." -Jesus
A The Holy Spirit is the Third Person of the Trinity, God at work in the world and in the Church even now.
Q How is the Holy Spirit revealed in the Old Covenant?
A The Holy Spirit is revealed in the Old Covenant as the giver of life, the One who spoke through the prophets.
Q How is the Holy Spirit revealed in the New Covenant?
A The Holy Spirit is revealed as the Lord who leads us into all truth and enables us to grow in the likeness of Christ.
Q How do we recognize the presence of the Holy Spirit in our lives?
A We recognize the presence of the Holy Spirit when we confess Jesus Christ as Lord and are brought into love and harmony with God, with ourselves, with our neighbors, and with all creation.
Q How do we recognize the truths taught by the Holy Spirit?
A We recognize truths to be taught by the Holy Spirit when they are in accord with the Scriptures.
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"It is written, 'My house shall be a house of prayer,' but you have made it a den of thieves." -Jesus