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This work brings together some mathematical demonstrations chosen for their elegance. It exposes brilliant ideas, unexpected connections and remarkable observations that shed new light on fundamental problems. According to the mathematician Paul Erdös, who himself suggested several of the themes presented, the proofs developed here deserve to be retained for inclusion in the Book where God would have listed the perfect demonstrations. Different fields are approached (number theory, geometry, analysis, combinatorics and graph theory) and the subject evokes both long established results and recently demonstrated theorems. In any case, their understanding requires only undergraduate level mathematical knowledge. This second edition offers a French translation of the revised and enlarged third English edition. It features two new chapters, many improvements, and new evidence. This book will appeal to all those interested in mathematics.