Here are some interesting links to the pages and documents explaining the mathematics behind the Rubik’s Cube.

§ http://web.usna.navy.mil/~wdj/rubik_nts.htm -- containing fairly interesting and advanced lecture notes by W. D. Joyner.

§ http://match.stanford.edu/bump/rubik.html -- Lecture notes on the Rubik’s Cube by Daniel Bump.

§ http://kociemba.org/cube.htm -- Cube Explorer, the Rubik cube solver with the description of the algorithm it uses.

§ http://www.geocities.com/jaapsch/puzzles/cubie.htp -- A virtual Rubik’s Cube and solver, written by Jaap Scherphius.

§ http://geometer.org/rubik/ -- Rubik’s Cube Simulator homepage.

§ Mathematics behind the Rubik’s Cube – a book by W. D. Joyner.

§ 26 moves suffice – a paper in which it is shown that 26 moves suffice to solve the Cube.

§ 25 moves suffice – a very recent paper, in which it is shown that 25 moves suffice to solve the Cube