I have here attempted to do for Determinants what has been already often enough done for various other branches of Mathematics, viz. to produce a text-book containing a full exposition of the theory in a form suitable for students, and having at intervals graduated collections of exercises to test the reader's progress and to prepare him for the succeeding stage of the subject.<br><br>The First Chapter refers to determinants of the second, third, and fourth orders, but only by way of introduction to what follows, and is written in the simplest possible style. The reader who has already some acquaintance with general algebraical reasoning may pass it over.<br><br>The Second Chapter treats of determinants in general and gives in one form or another all their important properties. At first, in the demonstrations recurrence is made to the definition oftener than is necessary for the purpose of mere proof, in order that thereby the reader may become thoroughly familiarized with the definition itself, which of course really contains the whole matter.