The Linux trademark belongs to Linus Torvalds. He has placed the Linux kernel under the GNU General Public License, which basically means that you may freely copy, change, and distribute it, but you may not impose any restrictions on further distribution, and you must make the source code available.
There is a FAQ for the GPL at: http://www.gnu.org/copyleft/gnu-faq.html.
This is not the same as Public Domain. See the Copyright FAQ, ftp://rtfm.mit.edu/pub/usenet/news.answers/law/copyright, for details.
Full details are in the file COPYING in the Linux kernel sources (probably in /usr/src/linux on your system).
The licenses of the utilities and programs which come with the installations vary. Much of the code is from the GNU Project at the Free Software Foundation, and is also under the GPL.
Note that discussion about the merits or otherwise of the GPL should be posted to the news group gnu.misc.discuss, and not to the comp.os.linux hierarchy.
For legal questions, refer to the answer: ("Where Are Linux Legal Issues Discussed?")