This volume provides an introduction to convolution operators with matrix-valued almost periodic or semi-almost periodic symbols. The basic tools for the treatment of the operators are Wiener-Hopf factorisation and almost periodic factorization. These factorisations are systematically investigated and explicitly constructed for interesting concrete classes of matrix functions. The material covered by this book ranges from classical results through to a first comprehensive presentation of the core of the theory of almost periodic factorization up to the latest achievements, such as the construction of factorisations by means of the Portuguese transformation and the solution of corona theorems. This book is addressed to a wide audience in the mathematical and engineering sciences. It is accessible to readers with basic knowledge in functional, real, complex and harmonic analysis, and it should be of interest to those who have to deal with the factorization of operators or matrix functions.