The author wrote a monograph 20 years ago on the construction of spin eigen­ functions; the monograph was published by Plenum. The aim of that monograph was to present all aspects connected with the construction of spin eigen­ functions and its relation to the use of many-electron antisymmetric wavefunctions. The present book is an introduction to these subjects, with an emphasis on the practical side. After the theoretical treatment, there will be many exam­ ples and exercises which will illustrate the different methods. The theory of the symmetric group and its representations generated by the different spin eigen­ functions is an other subject, this is closely related to the quantum chemical applications. Finally we will survey the calculation of the matrix elements of the Hamiltonian, using the different constructions of the spin functions. The closing chapter will deal with a new method that gained much importance recently; the spin-coupled valence bond method. Since the publication of Spin Eigenfunctions, nearly 20 years ago there have been many interesting developments in the subject; there are quite a few new algorithms for the construction of spin eigenfunctions. Moreover the use of the spin-coupled valence bond method showed the importance of using different constructions for the spin functions. The subject matter of this book has been presented in a graduate course in the Technion. The author is obliged to the graduate students Averbukh Vitali, Gokhberg Kirill, and Narevicius Edvardas for many helpful comments.