A MATHEMATICAL history of the right sort is much more than a mere bibliography, and in some respects is more valuable than a treatise on the subject with which it deals. It helps us to see how mathematical ideas originate, and how, as they become familiar, the symbolism by which they arc expressed becomes compact and appropriate. This is especially the case with determinants, because a determinant is essentially a comprehensive symbol, and it would perhaps be more proper to speak of the calculus than of the theory of determinants. It may seem strange, at first sight, to find a history so large as this dealing with a subject so limited; hut no one can complain that the author is either diffuse or irrelevant, and his work may be praised without restriction as a model of its kind.