Kinematics is a branch of mechanics that deals with the motions of a system of objects, so inverse kinematics would be its evil twin brother that deals with the non-motion of a system of objects. Well, not exactly.
In Max, a system of objects is a bunch of objects that are linked together. After a system is built and the parameters of the links are defined, the motions of all the pieces below the parent object can be determined as the parent moves using kinematics formulas.
Inverse kinematics (IK) is similar, except that it determines all the motions of objects in a system when the last object in the hierarchy chain is moved. The position of the last object, such as a finger or a foot, is typically the one you're concerned with. Using IK, you can then use these solutions to animate the system of objects by moving the last object in the system.
Before you can understand IK, you need to realize that another type of kinematics exists—forward kinematics. Kinematics solutions work only on a kinematics chain, which you can create by linking children objects to their parents.
Chapter 9, "Grouping, Linking, and Parenting Objects," covers linking objects and creating ...