The Catholics 

 Catholic Beliefs 

Authority, The Bible, Tradition, Etc
Catholics have various sources of authority: The Bible, Tradition, The Creeds, the Bishops, and the Pope, among others. Ultimately, Christ is our authority, but this authority has been passed from Christ to His Apostles. The Bible and Tradition come from the same Apostolic Deposit, and we do not pit them against each other. Thus the Church understands that the Bible must be interpreted, and the Church does so using the Tradition of the Apostles. The Catholic Church (and the Orthodox Church) has retained this Apostolic authority through Apostolic Succession, which is the passing down of authority from the apostles to their successors, our modern-day bishops. The pope, the bishop of Rome, has a first place among the successors to the apostles as the successor to Peter, the "Rock," and prince of the apostles, and under certain circumstances, has the grace to speak infallibly on issues of faith and morality. However, this does not mean everything the pope says is error free, or that the pope is sinless. While Catholics (and the Orthodox, many Anglicans, and the early Church) do not embrace sola scriptua
, the 16th century belief that the Bible alone is our final authority, Catholics hold the Bible in high regard as the word of God, and cannot teach contrary to the Bible's Teachings.

The Church: One, Holy, Catholic, and Apostolic
The Catholic church is the Church that Jesus Christ established. Thus the Church subsists in the Catholic Church. However, members of other Christian churches and denominations are also in communion with the Catholic Church by virtue of their sacraments. The Orthodox Churches possess fully valid sacraments, and are true particular Churches, whereas Protestant Christians are in communion with the Catholic Church on account of their baptism; still, this communion is impaired. The Church in one, because it is unified in Christ across regions and time periods. The Church is Holy on account of the grace of Christ given to it and the holy sacraments it provides. The Church is Catholic because it contains the fullness of the Apostolic Deposit of Faith, thus is it truly "according to the whole" and "universal." Finally, the Church is Apostolic because its Teachings and Authority come from the Apostles themselves.

Catholics believe that creation is good, and that God uses creation for His purposes, but that it has been marred by Original Sin, the result of the sin of the first humans. Catholic theologians as well as orthodox theologians have never agreed on one particular interpretation of the creation stories in the book of Genesis. A few early Christians read them literally, others allegorically, and others in light of the science of the day. Some read them all three ways at the same time. Catholics may interpret Genesis in a non-literal manner so long as the interpretation is faithful to Church Teaching. Thus, Catholics are free to understand Genesis literally, but also to read Genesis in light of modern scientific observations, so long as certain conditions are met.  For example, Catholics believe that God created the world from nothing and that He created the world through His Word, who became incarnate in Jesus Christ. Interpreting Genesis light of scientific observations may shock some Christians whose churches were founded during the modernist controversies of the 19th and 20th centuries. Surprisingly, insisting on an entirely literal understanding of the creation stories is actually a quite modern concept. 

God: The Trinity
Catholics believe in the Nicene Creed, and therefore believe in one God who exists as three persons ("person" in this usage means "an individual reality," not a human being). Essentially Catholics believe the Father, the Son, and the Holy Spirit are all God, one in substance and will, but distinct in some way, but not divided. In addition to an intellectual understanding of the Trinity, we are to develop a relationship with the Triune God through prayer and worship. The Trinity is not tritheism (the belief in three gods), but rather a dynamic monotheism. 

Jesus Christ: God and Man
Catholics believe Jesus is fully God and fully Man, with a human will and a divine will. He is the King of Cosmos, the Word of God, and the awaited Messiah of Israel. He was born of a virgin, Mary, suffered, was crucified, truly died, and rose again bodily, all for our sins. He ascended into heaven intercedes on our behalf before the Father. He will come again to judge the living and the dead. Jesus was a great teacher, and His teachings are the very teachings of God. 

The Catholic Church bases its moral Teachings on the message of Jesus. Morality boils down to love: loving God and loving our neighbors. If we truly love God (who himself is love) and neighbor, then our behavior toward ourselves and others will reflect this commitment. The Catholic Church teaches that we are to strive for holiness and perfection, since Jesus told us to be perfect as the Father is perfect (Matthew 5:48): Be perfect, therefore, as your heavenly Father is perfect. However, this is only accomplished with the help of God's grace. Catholics believe that we are called to turn from evil, and towards the good. This means turning away from actions and thoughts that are contrary to God's will. Most sins can be traced to the Seven deadly sins (Pride, Envy, Lust, Wrath, Gluttony, Greed, Sloth). Turning toward the good means developing virtue, that is a habitual and firm disposition to do good. The core virtues are divided into the Theological Virtues, which are the foundation of Christian moral activity (faith, hope, and love), and the Cardinal virtues around which all others are grouped (Prudence, Justice, Temperance, Fortitude). 
The Sacraments
The sacraments are divinely instituted signs that give the grace that they signify. In other words, sacraments are rituals and events through which God gives us grace. Catholics and Orthodox accept seven sacraments: Baptism, Holy Eucharist, Reconciliation, Confirmation, Holy Orders, Matrimony, and Anointing of the Sick.
Salvation and Grace
Catholics believe we are saved only by God's grace working in us. Thus we are justified, transformed from the state of unrighteousness into a state of holiness and the sonship of God, on account of Christ. Justification is the merciful and freely given act of God which takes away our sins and makes us just and holy in our whole being. This justification is given to us in the sacrament of baptism. Justification is the beginning of our free response to God, that is our faith in Christ and our cooperation with the grace of the Holy Spirit. Thus Catholics believe in salvation by grace alone, solely on account of the  work of Christ. However, neither Catholics nor Orthodox accept the reformation concept of forensic justification or "justification by faith alone.

Sin is the deliberate, freely chosen, transgression of divine law. There are two types of sin: mortal sin and venial sin. Sin that expels all charity from the soul is mortal, while sin that merely weakens charity is venial. For a sin to be mortal, the offense must be serious (have grave matter), and the act done freely, with deliberation. After committing a mortal sin, one must receive the sacrament of reconciliation before receiving communion. Sin entered the world through the disobedience of Adam and Eve. Original Sin is the privation of grace, inherited by all humans from Adam and Eve. Because of Christ's atoning death on the cross, we have the opportunity to have our sins forgiven, and this is not possible apart from God's grace. 

The Virgin Mary
Mary is the mother of Jesus Christ, fully God and fully man, thus she is called theotokos (God-Bearer) and "mother of God." Catholics, like Protestants, believe that Mary was a virgin when she gave birth to Jesus. However, Catholics and Orthodox believe that Mary remained a Virgin her entire life. Catholics believe that Mary was conceived without original sin in order to be a sinless bearer of God incarnate: Jesus Christ. This is known as the immaculate conception. This sinlessness was accomplished only on account of God's grace, and not on Mary's merits. The Orthodox too believe that Mary was sinless when bearing Jesus, but the moment at which she became sinless is debated. Catholics and Orthodox both believe that after Mary completed  the course of her earthly life, she was assumed into heaven, similar to the way the great saint Elijah was. Mary is the Mother of us and the mother of the Church, and just as Christ is the new Adam, Mary is the new Eve, who obeyed God where Eve disobeyed.