From History of the Christian Church, vol. 5: The Middle Ages 1049-1294. These are my notes. I am simply reporting what Schaff reported, though I think he is accurate.
Not all sacred rites, or sacramentalia, are the Seven Sacraments (703). All follow the Augustinian definition as “a visible sign of invisible grace.” There is a virtue inherent in the sacraments. They confer and confirm grace (continere et conferre gratiam).
God is the original cause of grace. The sacraments, per Thomas, are the instrumental cause (705).
The body of Christ is in the sacrament not quantitatively, but in substance. Not in dimensions but by a power peculiar to the sacrament. This is the doctrine of concomitance (717).
They argued that the whole Christ is in each of the elements, which justifies withdrawing the cup from the laity.
Penance and Indulgences
Penance deletes mortal sins committed after baptism (729). It has four elements (contrititon, sorrow of the soul, which negative part is attrition), confession, satisfaction, and absolution.
An indulgence simply mitigates the works of satisfaction needed for an absolution (737).
Sin and Grace
The flesh is tainted, being conceived in concupiscence. It is both taint and guilt (749).
Grace: man needs prevenient grace “to beget in him the disposition to holiness” (753).
Justification has four elements: 1) infusion of grace; 2) movement of the free will towards God; 3) the act of the free will against sin; 4) remission of sins.