I have an ATT U-Verse Wireless router supplying 5 computers throughout my home. It is hardwired to my main computer. I have three children of all ages, one of which has had a tendency to make poor decisions on websites, email, and internet chatting. We have discussed the issue, but I am of the 'trust but verify' mindset at this point
it will be a very good idea if you use a proxy server in your home network that will help you controlling web traffic and view the log file which contains the trace of connections I personally use Squid as a web Proxy and Sarg as a log analyzer .
Ok, so - you have a few options here..
It is my understanding that you're interested in monitoring the history of visited URL's on all of the computers on your small home network. If this is the case, you're in luck because this kind of feature is usually integrated directly onto the router for management purposes. Just log into your router's interface and find the area that contains a list of recently visited websites. You should also be able to block/allow urls from here too, if you so desire. Check your routers documentation for information about how to log into your router and other useful information.
I suppose you could do this all manually by firing up Wireshark or any other packet sniffer and "watch the wire" for yourself. I don't think this is what you're looking for, but I just thought I'd mention it anyway.
Alternatively you could install software on each of the client computers on your network which you want to monitor which will record activity on said computer, possibly in the form of logs/email. I don't recommend this if you can use either option above instead.
If you have a spare computer lying around with a spare NIC card, you could install Sophos UTM, which would sit behind your router and act as a hardware firewall. Amongst other things, you can see all URLs visited from any machine on your network. You can then of course block individual URLs or filter on things etc.
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