if you do not have a WIFI-Adapter for your Desktop PC, you could hook it up to your LAN of your Laptop and share the internet.

cp -v /etc/network/{interfaces,interfaces.bak}; # backup your existing network configuration
vim /etc/network/interfaces; # edit configuration

# setting up a bridge is similar to setting up a normal network-device
# setup bridge with fixed ip
auto br0
iface br0 inet static
    address 192.168.0.123
    netmask 255.255.255.0
    gateway 192.168.0.1
    bridge_ports wlan0 eth0
    bridge_fd 5
    bridge_stp no   # depending on your network, you might want to set this to yes

# now save and close
# run
/etc/init.d/networking restart; # restart networking service

you are now ready to connect a PC to your LAN port of your Laptop and share the Wifi-internet connection.

bridge_stp: https://wiki.linuxfoundation.org/networking/bridge_stp

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