The document describes Edmonds' algorithm for finding a maximum matching in a general graph. It constructs an M-alternating forest F where M is the current matching. If F contains adjacent outer vertices, it can augment M along the path between them. If F contains a blossom, it can shrink the blossom and reduce the graph size. Otherwise M is maximum. The algorithm repeats this process until no augmentations or reductions are possible, guaranteeing a maximum matching.