What were the main doctrinal disagreements between Luther and Calvin? Can anybody give an overview, please?
It should be noted that Luther and Calvin thought pretty highly of one another, despite their disagreements. Also keep in mind that when Luther nailed his 95 theses to the door, Calvin was less than 10 years old. It must also be remembered that a lot of what is taught under the banner of "Calvinism" today was not necessarily taught nor believed by Calvin, and the same applies to Luther and Lutheranism.
Salvation: They were both monergists, meaning they believed God completely accomplishes our salvation - human choice and deeds play no role. Luther taught the the will was bound until Christians are spiritually regenerated, and thus grace is resistible. Calvin believed that free will was gone permanently because God is completely sovereign, and thus His grace is irresistible. They essentially agreed on predestination, but Calvin believed that Christ died only for the elect ("limited atonement"), while Luther believed that Christ died for all humanity. Luther taught what is often called single predestination, which essentially means that God predestines people to heaven, but no one is predestined to damnation. Calvin on the other hand taught double predestination, that God predestines people either to heaven or hell.
Lord's Supper: Luther believed in the real presence of Christ in the Sacrament, but disagreed with the Roman Catholic doctrine of transubstantiation. Calvinists like to label this view as consubstantiation, but present-day Lutherans reject this label. Calvin affirmed the presence of the living Christ in the sacrament of the Lord's Supper by the action of the Holy Spirit, but disagreed with Luther's view because he felt it "localized" Christ to the elements. Calvin believed that Christ was "truly and efficaciously" present in the Lord's Supper, but in a spiritual sense, and through the mysterious intervention of the Holy Spirit, the communicant partakes spiritually of Christ's body" (cf. Institutes IV, 17, 18). It is argued whether Calvin's view is rightly called symbolic, or if it is a halfway point between Luther's view and the popular evangelical symbolic position. Either way, both Luther and Calvin felt that this was the biggest disagreement between them. Many Calvinists have argued that this disagreement was semantic and a result of clashing worldviews, while many Lutherans believe that these views are truly mutually exclusive.
Law/Gospel Emphasis: Calvin taught that God is absolutely sovereign, and man was created solely to bring glory to him. Luther did not necessarily disagree with this point, but his emphasis was much different. The motivation for glorifying God in Calvin's teaching was because this was man's obligation to God, which Luther felt was a Law-based focus. In Luther's teaching, while he didn't necessarily disagree with Calvin, man is privileged to serve God because of His grace and mercy, a Gospel-focused approach. This gets extended in each man's view of the Church (Calvin's emphasis of the visible vs. Luther's dual emphasis of the visible and invisible Church), but this is somewhat speculative. The Law/Gospel emphasis is a very subtle point, but most Lutherans believe it is extremely significant. Many modern-day Calvinists think this is an insignificant semantic argument (as well as with the Lord's Supper).
My Thoughts: This paragraph represents my opinion, and thus contains a Lutheran bias (I consider myself an Eastern Lutheran, which is somewhat oxymoronic). Having a Calvinist and a confessional Lutheran weigh in would be helpful to the discussion. Theology consists of a series of antinomies. They are not mere paradoxes that can be logically resolved, but both/and statements of truth. For instance,
- Jesus is completely divine and yet fully human.
- Jesus said "This is my body... this is my blood" and yet it is clearly bread and wine.
- God is completely sovereign yet man has free will.
- Christians are simultaneously sinners and saints (simul justus et peccator).
- Law & Gospel (You must be perfect, but your works contribute nothing to salvation).
- God is three and yet One.
Theological distinctives are often honest attempts to resolve these antinomies, but this places fallen human logic as judge over God's Word. It involves attempting to understand things that are beyond us, concepts for which our language and thinking are insufficient. Luther appeared to be more tolerant of antinomies, while Calvin often developed logical resolutions to many issues, viewing them as mere paradoxes (which only appear contradictory but can be logically resolved). In this sense, Luther was more tolerant of "mystery" while Calvin emphasized human logic more so. Both emphasized Western logic in many respects (Luther identified with Augustine's views on concupiscence which affects his belief of total depravity / original sin), but Luther vehemently attacked Aristotelian philosophy while defending Augustinian philosophy. Understanding Scholasticism and the philosophical underpinnings in German and French culture is crucial to understanding the deeper worldview issues influencing Luther and Calvin.
Overall I think both Luther and Calvin were honest, sinful men (just like the rest of us) who struggled with understanding God and His Word in their given historical and philosophical contexts. We are often unaware of our deepest biases, and this is no doubt the case for these men and for us as well. Their primary doctrinal disagreement centered in their views on the Lord's Supper, with significant philosophical underpinnings affecting this point of contention. It is my opinion that by embracing mystery and accepting the fact that our logic is fallen and corrupt, we will better "become partakers of the divine nature" (2 Peter 1:4).