Raspberry Pi Wifi Router/Repeater Howto (Hardware)

Verify Hardware Requirements

A wifi router or relay needs an AP cabable device.
A wifi relay needs a combined or additional managed device.

Examine wifi capable hardware.

	iw list
	# ...
        # Supported Ciphers:
        #   WEP40 (00-0f-ac:1)
        #   WEP104 (00-0f-ac:5)
        #   TKIP (00-0f-ac:2)
        #   CCMP (00-0f-ac:4)
        #   CMAC (00-0f-ac:6)
	# ...
	# Supported interface modes
	#   IBSS
	#   managed
        #   AP
	#   monitor
        #   P2P-client
        #   P2P-GO
        #   P2P-device
	# ...
	# Frequencies   ... 24xx MHz ... 5xxx MHz
	#
	# interface combinations are not supported
        # valid interface combinations:
        #   * #{ managed } <= 1, #{ P2P-device } <= 1, #{ P2P-client, P2P-GO } <= 1,
        #     total <= 3, #channels <= 2
        #   * #{ managed } <= 1, #{ AP } <= 1, #{ P2P-client } <= 1, #{ P2P-device } <= 1,
        #     total <= 4, #channels <= 1
	# ...

If AP and managed interface combinations are supported, one device might simultaneously be relay client and access point.
The Raspberry Pi Zero W and Raspberry Pi 3 AP/managed interface combination is restricted to 1 channel, and therefore unsuitable as single-device relay unless the LAN uses single fixed channel.)