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Tor is a proxy network used to improve anonymity and safety when using the Internet. Tor is free and based on open source code. Tor browser integrates the privacy system into a user experience.
Normal proxies often use a single-step connection, which means that even though they protect your personal information from being available to the websites you visit, your privacy might still be compromised by the owner of the proxy or by a hostile party hacking into the proxy server. Tor, on the other side, uses so-called onion layer routing, which means that instead of being routed through a single proxy, the data will be sent step-by-step in an encrypted circuit through a network of proxies. The circuit used often changes, and the proxies in the middle of the chosen route don't know the beginning or the end of the circuit; only which other proxies it receives data from and forwards to.
The end user runs a program called a Tor client on his computer. Using the official Tor Browser Bundle provided by the Tor Project is recommended. Anonymizing other applications is sometimes possible as well (through SOCKS proxy settings and/or torsocks) but user should be careful to prevent leaks. A filtering program (such as Privoxy) may still be useful for some use cases. Any Tor user with sufficient bandwidth can also choose to run a relay himself, letting other Tor users route traffic through his computer.
Tor website (downloads available)
"Tor" (Original BoyWiki Article)
"Tor (anonymity network)" Wikipedia Article