In 1910 I published a work under the title A History of the Theories of Aether and Electricity, from the age of Descartes to the close of the nineteenth century. When the original edition was exhausted, I felt that any new issue should describe the origins of relativity and quantum-theory, and their development since 1900. My opportunities were however not sufficient to enable me to prepare an accurate and fully-documented account of this very creative period, and I was compelled to lay the plan aside. Retirement from my professorial chair has made it possible for me to take up this project again ; it will occupy two volumes, of which this, the first, deals with the classical theories. The volume of 1910 has been to a considerable extent rewritten, with the incorporation of much additional material ; and in the second volume, the story will be continued to the present time.