Not a methodology! The Agile movement seeks alternatives to traditional project management. Agile approaches help teams respond to unpredictability through incremental, iterative work cadences, known as sprints. Agile methodologies are an alternative to waterfall, or traditional sequential development. Source: Agilemethodology.org
For more information about agile's origins, maniifesto and principles, see:
Becoming Agile:...in an Imperfect World by 
The Art of Agile Development by 
Adaptable Project Management - a Combination of Agile and Project Management for All (PM4A) by 
Hybrid Project Management by 
Agile Project Management for Dummies. 3rd edition by 
Agile Approaches on Large Projects in Large Organizations by 
Agile Project Management: Agile, Scrum, Kanban, and Extreme Programming by 
