The textbook and reference book literature in scattering theory and few body physics is by now rather obsolete, while there are no textbooks or reference books on most of the other topics in our book, including interactions in structured media. Important textbooks are outdated, excludes important topics or are focussed on applications in specific niche areas. Given this, a fresh, modern approach to the few-body problem, especially out of free space, and in generic (1,2 and 3) spatial dimensions is necessary. Moreover, the use and transition from few to many particles, allowing strong interparticle interactions to be treated non-perturbatively, is a very exciting field of research nowadays, and our book will present a self-contained reference book for researchers. Being very detailed in the methodologies followed, it will be very useful for graduate students getting into the field. With the information contained in this book, researchers and graduate students alike will be able to read and understand all the relevant and current research literature in the field and begin research on their own without the need for searching in the variety of fields where the theory presented in the book has been developed. In this book, we present a detailed account of the theory and methods to tackle the aforementioned systems from a bottom-up approach, which has been largely developed in the past decade by us and other authors. This begins with a full characterisation of strongly interacting few-particle systems, which can be dealt with accurately using a variety of analytical and numerical techniques. These non-perturbative solutions can be used to gain qualitative and quantitative insight into more complex problems, especially the many-body problem.