Contents: 1. A "true and proper" sacrifice: The background -- A purely sacramental sacrifice? -- The One Sacrifice of Christ -- The Council of Trent on the Sacrifice of the Mass -- The Eucharist as a natural sacrifice -- According to the Order of Melchizedek -- The debate of 1562. 2. Two Old Testament models of sacrifice: The three-part model of sacrifice -- The Offertory -- The priestly mediation -- The meal -- The three-part structure of the Mass -- The argument against the Offertory. 3. The Last Supper and the early Eucharist: The Last Supper as a Communion sacrifice of Bread and Wine -- The Last Supper as a Passover sacrifice -- The chronology of the Last Supper -- The Offertory of the Last Supper -- Matthew 5:23-24. 4. The Offertory in tradition: The Didache -- Saint Clement of Rome -- Saint Justin Martyr -- The subsequent history of the Offertory -- The decline of the Offertory in the West -- The reform of the Offertory after Vatican II -- Conclusion. 5. The Meal theory of sacrifice: The Meal theory of sacrifice -- The three sacrifices of Israel. 6. The Sacrifice of the Cross: The priestly mediation -- The Offertory of the sacrifice -- The Meal. 7. The Sacramental Sacrifice: One sacrifice/Many sacrifices -- The natural sacrifice -- The distinction of priesthoods -- The double offering -- The private Mass -- The active participation of the faithful -- Wit empty hands? -- The Sacramental Sacrifice -- The Offertory -- The Eucharistic Prayer -- Communion -- Conclusion.