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Box2D is a feature rich 2d rigid body physics engine, written in C++ by Erin Catto. It has been used in many games, including Crayon Physics Deluxe, winner of the 2008 Independent Game Festival Grand Prize. Many ports are available for Flash, Java, C#, Python, JavaScript, D, Scala and fixed point embedded devices.

There are specific manuals for AS3, and Python.

Instructions on compiling Box2D and creating your first world.

More in-depth guides for using Box2D.

Further reading
Official Manual Box2D Homepage FAQ Further Documentation Current TODO list User forums Ports to other programming languages Building Contributed code Known Issues WCK Documentation