In 1998, a group of individuals presented “open source” to relabel  free software as open-source software, for such software to become more mainstream in the corporate world. Software developers may want to publish their software with an open-source software license, so that anybody may also develop the same software or understand how it works. Open-source software generally allows anybody to make a new version of the software, port it to new operating systems and processor architectures, share it with others or market it. The aim of open source is to let the product be more understandable, modifiable, duplicatable, or simply accessible, while it is still marketable.
The Open Source Definition, notably, presents an open-source philosophy, and further defines a boundary on the usage, modification and redistribution of open-source software. Software licenses grant rights to users which would otherwise be prohibited by copyright. These include rights on usage, modification and redistribution. Several open-source software licenses have qualified within the boundary of the Open Source Definition. The most prominent example is the popular GNU General Public License (GPL). While open source presents a way to broadly make the sources of a product publicly accessible, the open-source licenses allow the authors to fine tune such access.
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Linux is a computer operating system and its kernel. It is one of the most prominent examples of free software and of open-source development: unlike proprietary operating systems such as Windows, all of its underlying source code is available to the public for anyone to freely use, modify, improve, and redistribute.
In the narrowest sense, the term Linux refers to the Linux kernel, but it is commonly used to describe entire Unix-like operating systems (also known as GNU/Linux) that are based on the Linux kernel combined with libraries and tools from the GNU Project and other sources. Most broadly, a Linux distribution bundles large quantities of application software with the core system, and provides more user-friendly installation and upgrades. Desktop environments such as GNOME and KDE are sometimes generically associated with Linux and are often referred to as such, but this is incorrect: a number of other operating systems, including FreeBSD use them.
Initially, Linux was primarily developed and used by individual enthusiasts. Since then, Linux has gained the support of major corporations such as IBM, Sun Microsystems, Hewlett-Packard, and Novell for use in servers and is gaining popularity in the desktop market. Proponents and analysts attribute this success to its vendor independence (the opposite of vendor lock-in), low cost, security, and reliability.
Linux was originally developed for Intel 386 microprocessors and now supports all popular computer architectures (and several obscure ones). It is deployed in applications ranging from embedded systems (such as mobile phones and personal video recorders) to personal computers to supercomputers.
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Debian, organized by the Debian Project, is a widely used distribution of free software developed through the collaboration of volunteers from around the world. Since its inception, the released system, Debian GNU/Linux, has been based on the Linux kernel, with many basic tools of the operating system from the GNU project.
Debian is known for its adherence to the Unix and free software philosophies, and for its abundance of options —the current release includes over fifteen thousand software packages for eleven computer architectures, ranging from the ARM architecture commonly found in embedded systems and the IBM s390 mainframe architecture to the more common x86 and PowerPC architectures found in modern personal computers. Debian GNU/Linux is the basis for several other distributions, including Knoppix and Ubuntu.
Debian is also known for its package management system, especially APT, the Advanced Packaging Tool, for its strict policies regarding the quality of its packages and releases, and for its open development and testing process. These practices afford easy upgrades between releases without rebooting and easy automated installation and removal of packages.
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Note – All the above information has been taken from http://www.wikipedia.org