The purpose of this book is to provide advanced students and mathematicians in other fields with the fundamental material in this subject. In addition, several applications of the type described above are included. In general we have tried to make this book self-contained, beginning with elementary concepts wherever possible; however, we assume that the reader is familiar with the basic definitions of homotopy theory: homotopy classes of maps and homotopy groups (cf. collection of spaces including projective spaces, flag bundles, and Grassmannians. Hilton [1] or Hu [1] for instance). Ordinary cohomology theory is used, but not until the end of Chapter V. Thus this book might be regarded as a fairly self-contained introduction to a "generalized cohomology theory".