I haven't used RedHat-based distros for years now but I remember that back when I switched to Debian-based distros I was equally confused about Debian's package management system. I didn't think, and still don't think, that dpkg and apt are documented that well. To answer your question: yum is to rpm as apt is to dpkg. But I've always found it weird that there's a difference between apt-get and apt-cache; in contrast, "yum install" and "yum search" use the same executable. The documentation concerning building Debian packages is often out of date and scattered all over the Internet with no clear central place. And finally there's this "aptitude" thing; I still don't understand why it exists and how it's different from regular apt.