This volume contains the proceedings of the Fourth Arolla Conference on Algebraic Topology which took place in Arolla Switzerland from August 20-25 2012. The papers in this volume cover topics such as category theory and homological algebra functor homology algebraic $K$-theory cobordism categories group theory generalized cohomology theories and multiplicative structures the theory of iterated loop spaces Smith-Toda complexes and topological modular forms.

This volume contains the proceedings of the conference on Manifolds, $K$-Theory, and Related Topics, held from June 23-27, 2014, in Dubrovnik, Croatia. The articles contained in this volume are a collection of research papers featuring recent advances in homotopy theory, $K$-theory, and their applications to manifolds. Topics covered include homotopy and manifold calculus, structured spectra, and their applications to group theory and the geometry of manifolds. This volume is a tribute to the influence of Tom Goodwillie in these fields.