I've, successfully gotten my Raspberry pi to operate as a web server, by connecting it to a router, identifying the ip and then accessing that ip from a browser on the same network. My question is, is it possible to replicate a similar functionality without the router ... where the client can directly connect to the raspberry pi.
If you're connecting directly, (e.g. Ethernet cable directly from PC to raspi), there should be no issue if both devices are configured with IP addresses that are on the same subnet.
For example, raspi IP = 192.168.1.2 and PC IP = 192.168.1.3 and netmask 255.255.255.0 for both. If a gateway needs to be configured, use 192.168.1.1. However, the gateway would not exist but should not be needed for off-subnet communications.