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 Theory

The 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.