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Debian is composed of free software mostly carrying the GNU General Public License. The operating system is developed by an internet collaboration of volunteers aligned with The Debian Project.
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Pros
Pro Very easy to customize the installation
Debian has a very flexible and customisable installation process. While many users choose to simply download and install a pre-built "live" installation, it is not only possible but quite easy to build a system from the ground up, installing only those packages that you need. This can be achieved by using the "mini" ISO to kickstart the installation of a bare-bones system, and then use apt to download your desktop of choice (KDE in my case), without all the bloatware that normally comes with it (ie utilities and tools you don't need or want).
Using this method, you can create a KDE-based Debian system (basic OS only, with a web browser thrown in for good measure) that is about a third of the size of the "live" CD - about 850MB, compared to about 2.6GB for the "live" CD. This also results in a faster boot time, and a more snappy and responsive system.
Pro Easy to find help with any problem
Debian is one of the oldest and most popular distros out there. Debian's popularity means that you will always be able to find a solution for your problem just by searching on Google, or if by chance nobody has had the problem you are having it's very easy to ask the community and quickly get a solution.
Pro Wide choice in desktop environments
Debian offers stable and testing CD images specifically built for GNOME (the default), KDE Plasma Workspaces, Xfce and LXDE. Less common window managers such as Enlightenment, Openbox, Fluxbox, GNUstep, IceWM, Window Maker and others can also be installed.
Cons
Con Software in "Stable" distribution tends to be outdated
Debian Stable (while certainly living up to its name) tends to have software that is older and often out of date. As a new release of Stable is brought out only once every 2 years or so, this can result in users being unable to access new features in certain applications (eg web browsers).
This can be mitigated by installing and using the "Testing" distribution instead, or even the "Unstable" distribution for those who just wanna watch the world burn. :) Unfortunately, these distributions (especially Unstable) tend to be buggier, and just aren't as smooth and trouble-free as Stable.