Christianity confesses the same absolute monotheism and then says something about its inner structure that Judaism and Islam both reject. The doctrine of the Trinity holds that God is one in being and three in persons, Father, Son and Holy Spirit, each fully God: not three Gods, and not three modes or masks of one person. It is not an appendix to the Christian doctrine of God. In the classical presentation it is the Christian doctrine of God, and the Catechism of the Catholic Church calls it the central mystery of Christian faith and life. An entry that treated it as a footnote to a shared monotheism would be misdescribing the tradition.
The formula was hammered out in the fourth-century controversies. The Council of Nicaea in 325 declared the Son homoousios, of the same being as the Father, against Arius, who held the Son to be the highest of creatures. The Council of Constantinople in 381 produced the creed still recited in most churches, extending the same confession to the Holy Spirit, "the Lord, the giver of life, who proceeds from the Father, who with the Father and the Son together is worshipped and glorified". Chalcedon in 451 settled a related but distinct question, how divinity and humanity are united in Christ, and is often confused with the Trinitarian settlement; it is not the same thing.
One later addition split the church. The Latin West inserted filioque, "and the Son", into the clause on the procession of the Spirit. The Greek East held the addition to be both theologically wrong and unilaterally made, and it remains among the principal issues between Rome and the Orthodox churches.
Christian theology insists throughout that the Trinity is not tritheism, and the insistence is not a modern apologetic afterthought, the anti-tritheist qualifications are as old as the doctrine itself. Whether that distinction survives contact with Jewish and Islamic monotheism is exactly what the fourth section of this entry is about, and it is not resolved there. One further point belongs here because it is easy to get wrong in both directions: the language of Father and Son is not treated in the tradition as one metaphor among many that could be swapped out, and the same Catechism nonetheless states flatly that God "is neither man nor woman: he is God".