Contains the proceedings of the conference on Manifolds, $K$-Theory, and Related Topics, held in June, 2014. The articles 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.

G. Arone and M. Ching, Manifolds, K-theory and the calculus of functors J. E. Bergner and P. Hackney, Diagrams encoding group actions on $\Gamma$-spaces S. Chang, S. Weinberger, and G. Yu, Contractible manifolds with exotic positive scalar curvature behavior E. D. Farjoun and Y. Segev, Relative Schur multipliers and universal extensions of group homomorphisms T. G. Goodwillie, Scissors congruence with mixed dimensions J. R. Klein and S. Tilson, On the moduli space of $A_\infty$-structures J. Noel, Nilpotence in the symplectic bordism ring K. E. Pelatt and D. P. Sinha, A geometric homology representative in the space of knots M. Szymik, Brauer spaces for commutative rings and structured ring spectra H. L. Tanaka, Bridgeland stability, 2-Segal spaces, and the Ran space of the line S. Tillmann and M. S. Weiss, Occupants in manifolds.