*Frontmatter, pg. i*Table of Contents, pg. v*Introduction, pg. 1*Notations and Conventions, pg. 16*Chapter I. The Algebra of Expressions, pg. 19*Chapter II. Crossnorms, pg. 25*Chapter III. Cross-Spaces of Operators, pg. 42*Chapter IV. Ideals of Operators, pg. 60*Chapter V. Crossed Unitary Spaces, pg. 65*Appendix I, pg. 134*Appendix II, pg. 148*References, pg. 151