Explicit Brauer Induction is a new and important technique in algebra, discovered by the author in 1986. It solves an old problem, giving a canonical formula for Brauer's induction theorem. In this book it is derived algebraically, following a method of R. Boltje--thereby making the technique, previously topological, accessible to algebraists. Once developed, the technique is used, by way of illustration, to reprove some important known results in new ways and to settle some outstanding problems. As with Brauer's original result, the canonical formula can be expected to have numerous applications and this book is designed to introduce research algebraists to its possibilities. For example, the technique gives an improved construction of the Oliver-Taylor group-ring logarithm, which enables the author to study more effectively algebraic and number-theoretic questions connected with class-groups of rings.