MATRIX is Australia’s international and residential mathematical research institute. It facilitates new collaborations and mathematical advances through intensive residential research programs, each 1-4 weeks in duration. This book is a scientific record of the eight programs held at MATRIX in 2018:- Non-Equilibrium Systems and Special Functions- Algebraic Geometry, Approximation and Optimisation- On the Frontiers of High Dimensional Computation- Month of Mathematical Biology- Dynamics, Foliations, and Geometry In Dimension 3- Recent Trends on Nonlinear PDEs of Elliptic and Parabolic Type- Functional Data Analysis and Beyond- Geometric and Categorical Representation TheoryThe articles are grouped into peer-reviewed contributions and other contributions. The peer-reviewed articles present original results or reviews on a topic related to the MATRIX program; the remaining contributions are predominantly lecture notes or short articles based on talks or activities at MATRIX.