Operators: An algebraic synthesis

From the preface: I have made an attempt in this book to develop a theory of operators from the concepts of abstract algebra. Although the level is roughly that of university entrance, I would hope that the book could be read with profit in the last school year. Equally well I hope that the book may give some pleasure to more mature mathematicians. The subject offers a challenge to precise habits of thought and I feel that I have myself learned a great deal in studying it. I derived considerable enjoyment from compiling the examples and exercises, particularly those in Chapters 7, 8 and 12, and I would urge the reader to try his hand at constructing his own identities. ... Mainly to help the beginner, the fundamentals of abstract algebra have been explained in the first four chapters. ...