This book deals with combinatorial aspects of epistasis, a notion that existed for years in genetics and appeared in the—eld of evolutionary algorithms in the early 1990s. Even though the first chapterputsepistasisintheperspective ofevolutionary algorithms and artificial intelligence, and applications occasionally pop up in other chapters, thisbookisessentiallyaboutmathematics, aboutcombinatorialtechniques to compute in an efficient and mathematically elegant way what will be defined as normalized epistasis. Some of the material in this book—nds its origin in the PhD theses of Hugo Van Hove [97] and Dominique Suys [95]. The sixth chapter also contains material that appeared in the dissertation of Luk Schoofs [84]. Together with that of M. Teresa Iglesias [36], these dissertations form the backbone of a decade of mathematical ventures in the world of epistasis. The authors wish to acknowledge support from the Flemish Fund of Scientific - search (FWO-Vlaanderen) and of the Xunta de Galicia. They also wish to explicitly mentiontheintellectualandmoralsupporttheyreceivedthroughoutthepreparation of this work from their family and their colleagues Emilio Villanueva, Jose Maŕa Barja and Arnold Beckelheimer, as well as our local T T Xpert Jan Adriaenssens.