What were the reasons for each mission? What did we achieve/learn from each mission?
There were seven attempts to land on the moon, Apollo missions 11-17; of which six were successful, the exception being Apollo 13 which famously suffered a mechanical accident en route. There have been no other manned missions to the moon. While the Soviet Union was attempting to do so in the early 1960's, its rockets were either too weak or too unstable to safely launch a manned capsule to the moon, so they didn't even attempt any manned flight beyond Earth orbit. More recently (and beyond the 20-year rule), several other nations have proposed lunar landings, but none of them have even gotten close to doing so.
In addition, two manned flights - Apollo 8 and 13 - circled the moon without landing; and one manned flight - Apollo 10 - descended within nine kilometers of the lunar surface and then ascended again without touching the surface.
Finally, numerous unmanned probes have landed on the moon, some of which have returned soil samples to Earth.