Abstract: E. Witt observed in the 1930's that suitable classes of quadratic forms form what is now known as the Witt ring of quadratic forms. After the work of C.M. Cordes, A. Fr$\ddot{o}$hlich, D.K. Harrison, H. Koch and R. Ware, finally M. Spira and J. Min$\acute{a}\breve{c}$ established in the 1980's and published in the 1990's a rather precise link between the Witt ring of quadratic forms and Galois theory. This connection has subsequently led to many important developments in this area. We will discuss quadratic forms, quaternion algebras, the Witt ring and Brauer group as well as these fascinating interconnections and the prospects for future research.

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