MQTT (MQ Telemetry Transport), which was invented by Dr Andy Stanford-Clark of IBM, and Arlen Nipper of Arcom (now Eurotech), in 1999. MQTT has become an OASIS (Organization for the Advancement of Structured Information Standards)standard in November 2014.
This post summarizes MQTT as specified in http://docs.oasis-open.org/mqtt/mqtt/v3.1.1/mqtt-v3.1.1.html.
The figure shows all the messages (and their parameters) between Publisher-Broker-Subscriber. It is divided into: Connection establishment, Subscribing to a topic, Publishing message with different QoS parameters, Connectivity management, and Disconnection.
For a summary of the messages and the changes expected to them in the upcoming version, use the cheat sheet in this MQTT cheat sheet.