The term Western Wall and its variations are mostly used in a narrow sense for the section traditionally used by Jews for prayer, and it has also been called the "Wailing Wall", referring to the practice of Jews weeping at the site over the destruction of the Temples.
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This is one of my main inspiration places in the world. I've not been there for a while and I miss it a lot. I'm not a religious person and I don't like the sound of systemized religion but that place always gives a few quiet moments that are followed by the feeling that all is really one.
A place to visit and understand. Complex situation as so many history myths legends whatever-you-call-it are the one on top each other. Follow the rules and respect the place, enjoy the traditions the cults...