Agile

Scrum

Scrum is a framework for developing, delivering, and sustaining complex products. It is based on the principles of transparency, inspection, and adaptation. Scrum is a lightweight framework that is easy to understand and difficult to master.

There are a lot of documentation about Scrum. However a lot of them are misleading. The best source of information about Scrum is the Scrum Guide.

Kanban

Kanban is a method for managing knowledge work with an emphasis on just-in-time delivery while not overloading the team members. Like Scrum, Kanban is a process designed to help teams work together more effectively.

Extreme Programming (XP)

Extreme Programming (XP) is a software development methodology which is intended to improve software quality and responsiveness to changing customer requirements.

You can check more details about XP on the Agile alliance website.