dpkg

List files in a package

dpkg -c <package_name>.deb
dpkg -L <package_name>

Find which package provides a file

dpkg -S /path/to/file

Get package info:

dpkg --info <package_name>.deb

List installed packages whose names contain foo:

dpkg -l '*foo*' | grep '^ii'

Post removal and post installation scripts are located at /var/lib/dpkg/info.