As with the empty tomb, the appearances of Jesus play a crucial role in the case for the Resurrection. If the disciples (and others) really had experiences of the risen Jesus, we require some explanation as to why they happened. Were they all having hallucinations? Were they being visited by Jesus’ unknown twin brother (yes, this is a real proposed theory)? Did Jesus actually survive the crucifixion and somehow manage to convince the disciples He was the risen Lord (Swoon Theory)? Or did God raise Jesus from the dead and appear to individuals and groups of people?
As I mentioned in my post on the Empty Tomb, this post is pretty long, so get your mind right. Second, The Son Rises and The Resurrection of God Incarnate influence much of what is said. Third, by no means is this an exhaustive list, there are many more arguments for the appearances of Jesus listed elsewhere (see Licona, Habermas, and N. T. Wright).
1 Corinthians 15
In 1 Corinthians 15, Paul cites a very old saying and lists the appearances of Jesus:
The sequence of “then” statements followed by “last of all” implies chronological ordering. This means that the other appearance traditions predate Paul’s (which most scholars agree happened within 6 years of Christ’s death), so they are all extremely early. The context of 1 Corinthians 15 makes it clear that Paul is giving historical accounts of meetings with Jesus. He reasons that what happened to Christ will happen in the future to those who have died (verse 18). The justification for this therefore must involve Christ coming back to life.
As Swinburne points out, we can judge the character of Paul simply by reading his letters. Paul comes across as a totally honest person. So if Paul endorses the saying quoted above, he must have himself believed it even after his meeting(s) with Peter and James. Lastly, Paul is not giving an exhaustive list of the appearances in his letter to the Corinthian church, only those that were most important or noteworthy (which explains why the appearances to the women go unnoted). We’ll briefly consider each appearance Paul mentions.
a) The appearance to Peter.
The appearance to Cephas, which is Aramaic for Peter, appears in both the credal saying quoted above and in Luke’s gospel:
Luke doesn’t go into detail on Peter’s appearance perhaps because he didn’t know the details and so, instead of making one up, briefly mentions it. Some scholars argue the linguistic peculiarities of Luke’s statement points to the fact that this too is an old Christian saying, maybe even going back to the same dating of the creed quoted by Paul. Furthermore, Paul spoke with Peter in Jerusalem six years after the event; one can imagine the topic came up at least once during their 15-day meeting. Paul couldn’t have affirmed the appearance to Peter if he didn’t believe it actually happened.
b) The appearance to the Twelve.
The appearance to the twelve is referred to in the credal statement and is also confirmed for us by Paul (who had access to and personal contact with the original disciples). It is also mentioned in both Luke and John:
Luke and John make it clear that the appearance to the Twelve (also mentioned by Paul) was both physical in nature and that it was the same Jesus who had been killed. In support of the appearance to the Twelve, we have multiple lines of evidence, from the creed quoted by Paul, to Paul himself, to both Luke and John.
c) The appearance to the five hundred.
Scholars note there’s a break in the creed at this point. This might indicate that the original creed ended and Paul is noting appearances known to him. If so, that wouldn’t undermine it’s reliability, since Paul likely received this information during his visit to Jerusalem. And as we’ve already seen, Paul’s testimony is bolstered by his character. Another peculiarity is that this appearance isn’t mentioned anywhere else in the New Testament. The natural inclination is to be skeptical at this point.
However, if Paul received this information on his trip to Jerusalem, he had plenty of time to check it’s veracity, yet he confirms for us that it happened. Moreover, note how Paul adds his own personal note that most of the 500 are still alive. The only reason for including that kind of comment would be to let people know they are there to be questioned. Paul could have never said something like that if he didn’t believe it occurred and that most of the 500 were still around.
d) The appearance to James.
The appearance to James, the earthly brother of Jesus, is another surprise. The gospels don’t relay this appearance, however Paul states (in Galations 1:19) he personally met James. So this information came directly from the source. What makes this so remarkable is that all of Jesus’ brothers–including James–were skeptical of Jesus’ divinity during his lifetime (Mark 3:21,31-35; John 7:1-10). Despite this, we have ample evidence that James played an important role in the Christian church very early on. The ancient historian Eusebius makes it clear that Jesus’ brothers performed missionary work in Galilee and Syria (for more on the relatives of Jesus, see this).
The most natural explanation of this dramatic change in James is the one that Paul records, namely that he experienced an appearance of Jesus. So not only do we have Paul’s rock-solid testimony confirming that it happened, we also have good evidence that James had a radical transformation after Jesus’ death which is explained by an appearance.
e) The appearance to all the apostles.
It’s not clear what group Paul has in mind here, however, these appearances are guaranteed historically since Paul was in contact with the apostles. Swinburne for instance thinks that many apostles were present at the appearance to the 500.
f) The appearance to Paul.
Lastly, Paul records that he too experienced an appearance of Jesus. Here’s how the author of Luke recounts Paul’s conversion:
“That the event really occurred is established beyond doubt by references to it in Paul’s own letters. He tells us that he was a Pharisee, extremely zealous for Judaism and perfectly obedient to the law of Moses (Galatians 1:14; Philippians 3:5-6). As a result of his earnestness, he was involved in persecuting the Christian movement, and he carried out his task with terrible vengeance (1 Corinthians 15:9; Galatians 1:13; Philippians 3:6). As he was near or in Damascus (Galatians 1:17), Christ appeared to him (1 Corinthians 9:1; 15:8; Galatians 1:15-16) and commissioned him to preach the gospel (Galatians 1:16; Colossians 1:25). After that event, which Paul considered his conversion (1 Corinthians 15:8; Philippians 3:7), he remained in Damascus three years before setting out as a gospel preacher in foreign lands (Galatians 1:17-21).” 
Paul gave up being a respected Jewish rabbi to live a life of constant hardship. Not only was he constantly laboring over the well-being of Christian churches throughout the Roman empire (as evidenced by his epistles), we are told he endured multiple scourgings, a stoning, three times he was shipwrecked, he often had no food and no place to stay, and eventually was executed in Rome. There can be little doubt the story of Paul’s life is amazing. Paul tells us why he did all this: he experienced the risen Jesus.
 Excerpt from The Son Rises.