dpkg

Install a .deb file
dpkg -i dropbox_2015.10.28_amd64.deb
Display installed packages
dpkg --get-selections
Display files installed by a package
dpkg -L <package>
Display installed version of a package
dpkg -s <package>
Find package owner for a file
dpkg -S /bin/bash
Reinstall files from a package

May be needed when you delete a vanilla configuration file: 

apt-get -o Dpkg::Options::="--force-confmiss" install --reinstall <package>
Force remove package in inconsistent state
dpkg --remove --force-remove-reinstreq <package>