In 2005, Dharam Ahluwalia and Daniel Grumiller reported an unexpected theoretical discovery of mass dimension one fermions. These are an entirely new class of spin one-half particles, and because of their mass dimensionality mismatch with the standard model fermions, they are a first-principle dark matter candidate. Written by one of the physicists involved in the discovery, this is the first book to outline the discovery of mass dimension one fermions. Using a foundation of Lorentz algebra it provides a detailed construction of the eigenspinors of the charge conjugation operator (Elko) and their properties. The theory of dual spaces is then covered before mass dimension one fermions are discussed in detail. With mass dimension one fermions having applications to cosmology and high energy physics, this book is essential for graduate students and researchers in quantum field theory, mathematical physics, and particle theory.