What evidence is there for the Resurrection of Jesus?

People have argued for the truth of Jesus' Resurrection on the basis of the biblical record alone, because there is no archaeological evidence and no extra-biblical evidence for his Resurrection.

The UCLA Institute on Primary Resources describes as primary resources that material which provides first-hand evidence of historical events. It says that they are a source of direct evidence that describes or documents an historical event from the perspective of someone who was there. On definitions such as this, the gospels would probably be primary resources if their authors saw, or participated in those events.

The Gospels of Matthew and John have long been regarded as eyewitness accounts, which means that they ought to be sufficient evidence. However, the four New Testament gospels were all written anonymously and were only attributed to the men whose names they now bear later in the second century. Uta Ranke-Heinemann says in Putting Away Childish Things, page 218, Matthew could not have been written by the Apostle Matthew, because it is incomprehensible that an eyewitness (Matthew) would choose to depend so radically on a non-eyewitness (the author of Mark). And Raymond E. Brown says in An Introduction to the New Testament, pages 368-9 that it is doubted by most scholars that John's Gospel was written by an eyewitness of the public ministry of Jesus.

As a result, people who have argued for truth of Jesus' Resurrection have used secondary, unattributed sources, rather than actual historical sources. In the absence of contemporary, historical evidence, it must be accepted by faith.

The Church of Jesus Christ of Latter-day Saints (LDS, or Mormons) has a unique addition to the already shared answers, which you might find interesting, at least.

This is not an attempt at a complete answer to the question - the question has already been answered by others who have much more education and knowledge than me. This is simply an additional piece of information from the LDS faith to consider as an addition to those answers.

Latter-day Saints view the Book of Mormon as historical fact. To them, the Book of Mormon itself is additional evidence of the Resurrection of Jesus Christ.

That's the quick answer, but I'm sure most people reading this won't know why, so here's a bit more to read for some of an explanation:

The Book of Mormon contains a 1000-year history of a group of people in the Americas from about 600 BC to 400 AD. The central message of the Book is that Jesus Christ was resurrected and that the testimony of the 12 apostles in Jerusalem is true. The most important moment in this book's history is when the resurrected Jesus Christ visits these people for 3 days. He tells them who he is and that he has finished the work his Father sent him to do, then he invites everyone to feel the nailprints in his hands and feet so that they can know that he is the God of Israel that was crucified (see 3 Nephi 11:10-15)

The Book of Mormon was never intended to stand on its own as the testament of Jesus Christ. It was always meant to stand beside the New Testament as another testament of Jesus Christ (thus the subtitle, Another Testament of Jesus Christ). The people in the Book knew that the mortal Jesus Christ would not live among them, but they believed that after he was resurrected he would come visit them. Here are two important passages about the role their knowledge of Jesus Christ plays:

First, a man named Nephi wrote a vision he received. Among the things he saw was the record of the prophets and of the 12 apostles (the Bible) being brought to the Americas and shared with his people - and the role that the record of his people (the Book of Mormon) would play beside that:

1 Nephi 13:39-40

39 And after it [the Bible] had come forth unto them I beheld other books, which came forth by the power of the Lamb, from the Gentiles unto them, unto the convincing of the Gentiles and the remnant of the seed of my brethren, and also the Jews who were scattered upon all the face of the earth, that the records of the prophets and of the twelve apostles of the Lamb are true.

40 And the angel spake unto me, saying: These last records [Book of Mormon], which thou hast seen among the Gentiles, shall establish the truth of the first, which are of the twelve apostles of the Lamb, ... and shall make known to all kindreds, tongues, and people, that the Lamb of God is the Son of the Eternal Father, and the Savior of the world; and that all men must come unto him, or they cannot be saved.

Second, Mormon, who lived around 400 AD and compiled the Book of Mormon, speaks to any of his people who might read the record. He talks about the Bible:

Mormon 7:8-9

8 Therefore repent, and be baptized in the name of Jesus, and lay hold upon the gospel of Christ, which shall be set before you, not only in this record but also in the record which shall come unto the Gentiles from the Jews, which record shall come from the Gentiles unto you [the Bible].

9 For behold, this [Book of Mormon] is written for the intent that ye may believe that [Bible]; and if ye believe that ye will believe this also; and if ye believe this ye will know concerning your fathers, and also the marvelous works which were wrought by the power of God among them.

So, to the main point. The Bible is a record from the Old World. The Book of Mormon is a record from the New World. The Book of Mormon peoples had no contact with Jerusalem or the apostles or any "Christian" missionaries during and after Christ's mortal ministry. However, the Book claims that these people saw the resurrected Christ.

The Book of Mormon itself stands as evidence of Jesus Christ's resurrection. The people in it could not have testified of his resurrection unless he came and visited them himself - as a resurrected being. It establishes the truth of the first witness, the New Testament, by providing the world with a second witness of the Resurrection of Jesus.

The resurrection of Jesus Christ from the dead is central to the Christian message. Without it, Christianity would be just another religion. What makes the case so compelling for belief? Here are several ideas to consider.

God knew how hard it would be for us to believe someone could rise from the dead, so he told us throughout the Old Testament that he will raise a particular person at a particular time. Those passages, called prophecies, tell us that Jesus would be in the ground only three days and that his body would not decompose (Acts 2:24-32). It tells us that Jesus would die with pierced hands and feet, foreshadowing the torture of the cross (Psalm 22:16), a method of capital punishment which had not been in existence at the time of the prophecy.

Resurrection was not a fluke occurrence, but planned. Jesus himself spoke to his followers about dying and rising from the dead. They did not understand what he meant, for they had supposed the Messiah of whom God prophesied would live long enough to overthrow the Roman yoke. His resurrection was not a secret, for Jesus shared it repeatedly to his disciples. Jesus used his resurrection as a sign that his ministry and words would be vindicated. If he had not risen from the dead, he would be just another good man among historical figures who told people to live a good life. Because he did rise from the dead, his message has startling urgency.

God had a reason for Jesus’ death and resurrection. God had established a means through which his people, the Israelites, could be “cleansed” of their sins, and by which his holy presence could remain in their midst: he instituted animal sacrifices. When a person sinned, he would come to the priest with an animal specified in the law, such as a lamb, place his hands on the animal, and thus transfer his sins to the substitute, then kill the sacrifice. The sinner would see with his own eyes that the animal bore the penalty of death for what the sinner had done. This institution of animal sacrifices looked forward to the sacrifice of Jesus, who became the Lamb of God on the cross, suffering in our place. In Isaiah 53, we see ahead of time Jesus’ substitutionary sacrifice fully revealed. Jesus was the ultimate sacrifice who died for the sins of the whole world. Jesus died so that we would not have to suffer sin’s punishment in the next life. His death rendered all subsequent animal sacrifices superfluous.

Many people reject the message of the resurrection simply because they do not believe the Bible. However, the resurrection is not a religious issue. It is a historical issue. It occurred in a particular time and place, with particular people impacted by the event. The early Christians lived and died for witnessing to a singular event – the resurrection of Jesus Christ. They did not stand for a particular morality or ethics, but a person who was raised up from the dead.

Jesus’ enemies acknowledged that he had indeed died and had been buried in a tomb. They requested of Pilate “that the tomb be made secure until the third day, lest His disciples come by night and steal Him away, and say to the people, ‘He has risen from the dead.’ So the last deception will be worse than the first” (Matthew 27:64b).

When Jesus died, his followers took down his body from the cross and prepared his body for burial. They had plenty of opportunity to ascertain his condition.

The resurrection of Jesus was central to early evangelistic preaching, and, predictably, it was not readily believed. “And when they heard of the resurrection of the dead, some mocked, while others said, ‘We will hear you again on this matter'” (Acts 17:32). The stories that follow Jesus’ death and resurrection credibly relate the believers’ and unbelievers’ conflict over the message. All the encounters had the ring of truth.

Jesus’ resurrection appearance dramatically changed the disciple’s lives. Immediately after Jesus’ death and before his resurrection, they were cowering in an upper room “for fear of the Jews” (John 20:19b). Within days of his miraculous bodily appearance to them, they were standing boldly in the face of opposition, confirming that this “This Jesus God has raised, up, of which we are all witnesses” (Acts 2:32). “Therefore let all the house of Israel know assuredly that God has made this Jesus, whom you crucified, both Lord and Christ” (Acts. 2:36).

No attempt was made by the enemies of the disciples to prove that Jesus’ death and subsequent appearances were a hoax. They presented no evidences to disprove his miracles or the miracles of his disciples. Instead, the leaders attacked the followers themselves and sought to stop their message. The witnesses were so numerous that Paul the apostle, in writing to the Corinthians, noted that many of the five hundred who saw Christ’s post-resurrected appearances were still alive at his writing to confirm or deny the gospel (1 Corinthians 15:6). Christ’s death, burial, and resurrection were historically attested to. Historians have more evidences for the death and burial of Jesus than for any other ancient historical character.

Consider that the Jews have been keeping the Sabbath, wearing the yarmulke, being circumcised, meeting in synagogues, and keeping other practices for thousands of years. Even when persecution scattered them throughout the world, they kept their traditions. The fear of violence and living in foreign lands far from their homeland did not stop their practices. Yet something happened two thousand years ago, at the time of Jesus, that changed their practices. In a short period, the Jews had abandoned the yarmulke, circumcision, and animal sacrifices – something that violence and death had not been able to change for thousands of years.

The best historical evidence to Jesus resurrection would have to be given by someone with nothing to gain from it. As a follower of Christ and believer that He is the Messiah, I have something to gain from telling everyone I've seen the resurrected Jesus - it gives proof and validity to my beliefs; It makes me "not crazy" to have followed Him. This would apply to the 10 and the women who visited the tomb.

But the fact that Paul, who was dedicated to the Persecution of the Church, and therefore who had nothing to gain from Jesus' Resurrection bore witness is the strongest proof for His resurrection. I would say the 500 men who saw Him at one time is also great proof.