(Image taken from a t-shirt available from Wrath and Grace)
The resurrection of Jesus Christ is the central tenet of Christianity. Without it, Christianity crumbles. Or, to put it another way, if it could be proven that Jesus did not rise from the dead, Christianity would cease to exist.  Why? Because those who served as the foundational stones of the Church, the Apostles,  would be proven to be false witnesses,  since they clearly testified that Jesus rose from the dead. Jesus sent them to preach to the very people who had Him crucified – the Pharisees and Jewish people – and proclaim His resurrection with the power to perform signs and wonders to back up their claim. It was the number one topic of their preaching in the Book of Acts.
Since Luke, the author of the Gospel bearing his name and the book of Acts, tells us that Jesus “shewed himself alive after his passion by many infallible proofs” , let’s look at some of those proofs primarily from his second volume.
Many of these proofs center on the disciples’ shared experiences, meaning they could not have dreamed or hallucinated Jesus’ resurrection.
What They Saw
First, according to Acts 1:3, Jesus appeared to them multiple times over a 40 day period. They occurred during this definite period of time, and then after He ascended into heaven, the appearances stopped – with the notable exception of Paul, to whom Jesus appeared “as of one born out of due time.”  This displays consistency among their testimonies. None of them had a private visitation at a later date to receive additional revelation, but once Jesus ascended, the visitations ended.
Multiple people witnessed Jesus alive after His death. 1 Corinthians 15:6 asserts that more than 500 people saw Jesus at the same time, possibly at His Ascension. Two people do not have the same hallucination experience, much less 500!
What They Heard
Acts 1:3 also says that Jesus spoke with them, and verses 4-9 records some of what He said. All of the Apostles heard the same thing and obeyed Jesus’ command to stay in Jerusalem. Had this been a hallucination, their accounts would differ, but they all heard and preached the same message.
More Shared Experiences
Jesus assembled with the disciples in verse 4, and we know Jesus ate with them on at least two occasions.  Had they hallucinated Jesus appearing and eating before them, when the experience was over, the food would have still been there. Because hallucinations don’t eat! 
On the night before Jesus was crucified, He promised to send the Holy Spirit after He would rise from the dead and ascend to the Father.  In between His Resurrection and Ascension, He reiterated that promise.  So, when the Holy Spirit came as recorded in the second chapter of Acts, empowering His Apostles to speak in languages they didn’t know and to boldly preach the Gospel, in fulfilment of this promise, it served as proof that Jesus in fact rose from the dead.
Lastly, the Book of Acts itself exists as evidence of Jesus’ resurrection. Luke wrote that his first volume, his Gospel, was about “all that Jesus began both to do and teach,”  implying that this second volume would be about what Jesus continues to do through His Church. Jesus’ ongoing work through the Church in Acts and throughout history prove He’s alive!
How can I make this claim? As I said at the beginning, the disciples preached the resurrection of Jesus to the very people who had Him crucified, who hated Him. Had there been any evidence to the contrary, His enemies wouldn’t have hesitated to present it and shut the Apostles up.  But since they couldn’t, they tried persecuting them. That didn’t work either, but only helped the Gospel spread even more.
One skeptical theory is that the disciples made these experiences up. However, that theory doesn’t fly when one considers that every one of them were persecuted and/or martyred for their confession of Christ. People die for lies all the time, but people don’t die for what they know is a lie. If the disciples had concocted the story of Jesus’ resurrection, at least one of them would have caved and admitted to it once the beating started. Yet none of them did. This serves as a powerful piece of evidence in favor of Jesus’ resurrection.
These are only a few proofs that Jesus did in fact rise from the dead. If we examined further, we could uncover more, but these are sufficient for us to determine on the basis of the evidence that Jesus did in fact rise from the dead. Returning to the verse cited at the beginning, Acts 1:3 says that Jesus “shewed himself alive after his passion by many infallible proofs.” This is the only time the word “infallible” occurs in the New Testament, and it means “that from which something is surely and plainly known; on indubitable evidence, a proof; demonstrable proofs” . In modern vernacular, we could say that Jesus proved to His disciples that He was alive beyond a shadow of a doubt. So we can definitively say, “But now is Christ risen from the dead…” . The disciples’ experience was not a hallucination, and Jesus was not a mirage, spirit, phantom, or zombie.
He is risen!
 If Jesus is still dead, not only would Christianity be, but so would we be, in our sins. (1 Cor. 15:17)
 Ephesians 2:20
 1 Corinthians 15:15
 Acts 1:3, italics added
 1 Corinthians 15:8
 Luke 24:41-43, John 21:1-15
 Neither do spirits or ghosts, so incidentally this also proves that Jesus rose from the dead bodily.
 John 16:7, 14:16-20
 Acts 1:5, 8
 Acts 1:1, italics added
 His enemies knew Jesus rose from the dead and tried to bribe the Roman soldiers to keep them quiet.
 Strong’s Concordance
 1 Corinthians 15:20