Unless stated otherwise, all information herein is taken from Towers of Midnight, Chapter 40.
Mah'alleinir, in the Old Tongue "He who soars", is a hammer forged by Perrin and strengthened by Fager Neald, with a circle of Wise Ones and Jur Grady. It is the first known weapon to use the One Power in its making since the Age of Legends. Part of its strength comes from Neald keeping it at exactly the correct temperature, so that Perrin can be more careful about folding and shaping, rather than trying to do everything in the few moments of perfection, but others come from specific weaves Neald uses. Although he is still able to create Power forged weapons afterwards, he is unable to recall exactly what he did, so Mah'alleinir remains unique (This passage needs a reference). Its touch burns Trollocs (ToM, Ch. 41). The name is similar to that of the hammer of the Norse God Thor, Mjölnir.