This selection of papers from the Beijing conference gives a cross-section of the current trends in the field of fixed point theory as seen by topologists and analysts. Apart from one survey article, they are all original research articles, on topics including equivariant theory, extensions of Nielsen theory, periodic orbits of discrete and continuous dynamical systems, and new invariants and techniques in topological approaches to analytic problems.

Bifurcation theory for metric parameter spaces.- A fixed point index approach to some differential equations.- Topological characteristics of infinite - dimensional mappings and the theory of fixed points and coincidences.- Fixed points of map extensions.- Two vignettes in fixed point theory.- Index theory for noncompact group actions with applications to Borsuk-Ulam theorems.- Fuller's index for periodic solutions of functional differential equations.- Simple variational methods for unbounded potentials.- The lefschetz function of a point.- Nielsen-type numbers for periodic points, I.- Braids and periodic solutions.- Coincidences for Grassmannian and associated spaces.- Congruences for fixed point indices of equivariant maps and iterated maps.- Clifford asymptotics and the local lefschetz index.- On solutions of frame mappings into manifolds.- The number of periodic orbits of smooth maps.- Parametrized Borsuk-Ulam theorems and characteristic polynomials.- On an example of Weier.- The positive solutions of quasilinear elliptic boundary value problem.- A relative Nielsen number for the complement.