First, Agile Software Development is NOT a methodology. It would rather describe it as a movement, perhaps a
philosophy.
Scrum and XP both are approaches (I hesitate to say "processes"), that contributed to the Agile movement.
Lean Software Development is inspired by Lean Manufactoring, which is inspired by the Toyota Production System. From what I know, it looks like a rather high level description of the forces of software development, which makes it look to me at rather a similar level as the Agile movement.
Kanban is a project management process that is also inspired by a process of the same name from the Toyota Production System. It is roughly at the same level as Scrum, and can be seen as an alternative to it. There is also a hybrid process called Scrumban.
Lean and Kanban are generally considered to be very compatible with the Agile mindset. I would consider them part of the Agile family, but I have heard of people who would disagree.
Does that help?
