Mathematicians often speak of the unity of their subject, whether to praise it or lament its passing. This book traces the emergence of such a unity from its nineteenth century origins in the history of linear ordinary differential equations, especially those closely connected with elliptic and modular functions. In later chapters the book is concerned with the impact of group theoretical and geometrical ideas upon the problem of understanding the nature of the solutions to a differential equation. So far as is possible, the mathematics is developed from scratch, and no more
than an undergraduate knowledge of the subject is presumed. It is my hope that this historical treatment will reacquaint many mathematicians with a rich and important area of mathematics perhaps known today only to specialists.