Thousand of persons now are able to solve Rubik's Cube, but the solution manuals they have been using do not give them a comprehension of what they have been doing. This book supplies such a comprehension. The handbook proceeds from topics easily understandable to the layman, to topics suitable for a junior-high-school or high-school course in math, and on to subjects appropriate for a college course in modern algebra. Chapter Tree is a solution manual for those who do not yet know how to solve the cube. This solution is an intuitive one that does not require memorisation of the formulas. It may be among the fastest solutions published, since the authors retain an open 'working space' to avoid having only a restricted area for the last pieces to move in. Movements of the cube exemplify a fascinating but abstract field of mathematics known as group theory. Manipulation of the cube makes the hard-to-understand ideas of this field concrete and understandable in the manner of no other device yet invented.