This volume outlines the proceedings of the conference on 'Quadratic Forms and Their Applications' held at University College Dublin. It includes survey articles and research papers ranging from applications in topology and geometry to the algebraic theory of quadratic forms and its history. Various aspects of the use of quadratic forms in algebra, analysis, topology, geometry, and number theory are addressed. Special features include the first published proof of the Conway-Schneeberger Fifteen Theorem on integer-valued quadratic forms and the first English-language biography of Ernst Witt, founder of the theory of quadratic forms.
Galois cohomology of the classical groups by E. Bayer-Fluckiger Symplectic lattices by A.-M. Berge Universal quadratic forms and the Fifteen Theorem by J. H. Conway On the Conway-Schneeberger Fifteen Theorem by M. Bhargava On trace forms and the Burnside ring by M. Epkenhans Equivariant Brauer groups by A. Frohlich and C. T. C. Wall Isotropy of quadratic forms and field invariants by D. W. Hoffmann Quadratic forms with absolutely maximal splitting by O. Izhboldin and A. Vishik 2-regularity and reversibility of quadratic mappings by A. F. Izmailov Quadratic forms in knot theory by C. Kearton Biography of Ernst Witt (1911-1991) by I. Kersten Generic splitting towers and generic splitting preparation of quadratic forms by M. Knebusch and U. Rehmann Local densities of hermitian forms by M. Mischler Notes towards a constructive proof of Hilbert's theorem on ternary quartics by V. Powers and B. Reznick On the history of the algebraic theory of quadratic forms by W. Scharlau Local fundamental classes derived from higher $K$-groups: III by V. P. Snaith Hilbert's theorem on positive ternary quartics by R. G. Swan Quadratic forms and normal surface singularities by C. T. C. Wall.