1) Calvinism teaches the doctrine of predestination, that God predestines some to be saved and others not.
2) The core doctrines of Calvinism include: total depravity of man, unconditional election by God, limited atonement of Christ's death, irresistible grace, and perseverance of the saints.
3) The doctrines are logically connected - if man is totally depraved and unable to be saved without God's intervention, then God must predestine some to salvation and Christ must have died only for the elect. Once saved, one is always saved.