Joe: General answer
General answer: yes. It's called "wireless bridge" mode. Practical answer: you can't do it with most commercial routers, as-is. You'll usually need something with custom firmware, such as DDWRT. It does work, but you'll be limited by the Wi-Fi connection, however good or bad it is. Guessing why you're asking answer: You should look into "Ethernet over powerline adapters". Plug one in to a wall outlet near your main router, plug another in to an outlet in your room, and use Ethernet cables to connect the router and your computer. I got mine for about $50, and the performance is far better than the wireless bridging I was using before.
Yes. I do that in my garage, since I didn't want to run a cable. Wifi router in the garage is reconfigured to connect to the wifi router in the house as a bridge and the ethernet ports on the back of the garage router are now live for connections. Modem---HouseWIFi >>>> <<<GarageWiFi---wired connection to PC
Richard: I use a TP-Link TL-WA850RE http
I use a TP-Link TL-WA850RE http://www.tp-link.us/products/details/cat-5508_TL-WA850RE.html Modem/Router - WiFi - TL-WA850RE - Ethernet - TV My smart TV only has Ethernet networking. The manufacturer's WiFi adapter costs around $100, while companies like Best Buy advertise the TL-WA850RE for around $20. Although it is a WiFi range extender, I have the extension network disabled and use it as a WiFi to Ethernet adapter. I hope this helps.