Spinors in Four Dimensional Spaces Without using the customary Clifford algebras frequently studied in connection with the representations of orthogonal groups spinors are developed in this work for four dimensional spaces in a language analogous to the spinor formalism used in relativistic spacetime. This systematic and self contained book provides very useful details as to how spinors work and includes many interesting examples of why they are useful such as applications in Yang Mills theory. This work will serve graduate students and researchers in mathematical and theoretical physics it is suitable as a seminar text a reference book and a self study guide. Reviews from the author`s previous book 3 D Spinors Spin Weighted Functions and their Applications: In summary...the book gathers much of what can be done with 3 D spinors in an easy to read self contained form designed for applications that will supplement many available spinor treatments. The book...should be appealing to graduate students and researchers in relativity and mathematical physics. Mathematical Reviews The present book provides an easy to read and unconventional presentation of the spinor formalism for three dimensional spaces with a definite or indefinite metric...Following a nice and descriptive introduction chapters 2 4 are devoted to spin weighted functions and their applications while chapters 5 and 6 collect all the standard material on spinor algebra and spinor analysis respectively. The final chapter contains some applications of the formalism to general relativity. Monatshefte für Mathematik