How to set up a single unified communal network. (ie large building, multiple access points, single network)

I am a relative networking novice so excuse incorrect terminology but I need to transition a communal living house network into more of a commercial/unified network and am looking for advice on hardware/technique. Background: The building is 3 stories tall and houses 40 residents in personal rooms with communal living space. This leads to well over 40 connected devices between phones, computers, and gaming from residents and guests all on the single network. Currently each room has an Ethernet port and many have set up their own personal wireless networks with a small router. In addition to this there are 3 unconnected public routers throughout the building leading to many dead spots of wireless connection and continuous switching of network choice. I plan to eliminate the personal networks and create one unified wireless network. I believe the current modem to be over 6 years old and the routers are cheap with limited range. Am I correct that I can set up a single network with multiple routers as access points to extend coverage? Are there recommended pieces of hardware for this or resources to guide the setup?