In the first edition of Volume 1 of The Art of Computer Programming, Donald E. Knuth introduced the MIX machine language: a teaching tool that powerfully illuminated the inner workings of the algorithms he documents. Later, with the publication of his Fascicle 1, Knuth introduced MMIX: a modern, 64-bit RISC replacement to the now-obsolete MIX. Now, with Knuth's guidance and approval, Martin Ruckert has rewritten all MIX examples, exercises, and exercise answers from Knuth's Volumes 1-3 in MMIX, thus completing the MMIX update to the original classic. Building on contributions from the international MMIXmasters volunteer group, Ruckert fully addresses MMIX basic concepts, information structures, random numbers, arithmetic, sorting, and searching. He has checked all of this supplement's 15,000 lines of code with the MMIX assembler for syntactic correctness and has successfully executed every line with appropriate test cases. The MMIX Supplement should be read side by side with The Art of Computer Programming, Volumes 1-3, and Knuth's Fascicle 1, which introduces the MMIX computer design and assembly language. Throughout, this supplement contains convenient page references to corresponding coverage in the original volumes. To further simplify the transition to MMIX, Ruckert changed only as much as was necessary to illuminate the new system. The resulting text will serve as a bridge to the future, helping readers apply Knuth's insights in modern environments, until his revised, "ultimate" edition of The Art of Computer Programming is available (anticipated in the year 2020). From Donald E. Knuth's Foreword: "I am thrilled to see the present book by Martin Ruckert: It is jam-packed with goodies from which an extraordinary amount can be learned. Martin has not merely transcribed my early programs for MIX and recast them in a modern idiom. He has penetrated to their essence and rendered them anew with elegance and good taste. His carefully checked code represents a significant contribution to the art of pedagogy as well as to the art of programming...I encourage serious programmers everywhere to sharpen their skills by devouring this book."