I updated my Ubuntu from 15.10 to 16.04 LTS. Very good release, I'm really happy with it, for sure it is much more stable than the 15.10 was. However, when opening the package manager I cannot find most packages. I had added all the most common repos in 15.10 and I am able to install any package I need using sudo apt-get install, however I cannot find those packages when using the new UI in the package manager. For instance, I've installed R and Idle3 using the command line, but if I look for those programs in the package manager using the search box nothing comes up. How can this be?
SnapOverflow
I assume with "I had added all the most common repos in 15.10" you mean third-party repositories like PPAs? Repositories are specific for different Ubuntu releases. For example, the (arbitrarily chosen) Cinnamon Nightly PPA is available for Ubuntu releases from Trusty to Yakkety. Each of these releases gets a different set of packages from the PPA.
Because of that, third-party repositories get routinely disabled in the upgrade process (when you switch from one Ubuntu release to another). After the upgrade, you can look through your third-party repos. Some you can just switch to the new Ubuntu release you're using (for example from "wily" to "xenial"), because the repo maintainer offers the repo for that version as well. Some repos may have become obsolete, because the packages you added the repo for are now part of the main Ubuntu release. Some repos are not available for the Ubuntu release you're running now, so you can't use them any more.