Matrix is kind of like a federated IRC system and Riot is a web and mobile interface to the Matrix system.
Matrix IRCd - Bridge to IRC.
What is Matrix?
sytest - Black-box integration testing for Matrix homeservers.
Unofficial list of public Matrix servers
Matrix GSOC ideas
Riot Web - Web client for Matrix.
Ruma - Matrix homeserver written in Rust.
Nheko - Native desktop client for Matrix.