The tiling book : an introduction to the mathematical theory of tilings Mathematics is often seen as a collection of subjects each learned one at a time. Although those fields rarely overlap they are all subsumed under the heading of mathematics as they all rely on rigorous logical deductions from a set of axioms. But in fact there are numerous overlaps and interconnections between fields. And often the most interesting mathematics comes about when connections are made across the sub disciplines. Tiling theory happens to be an area where many of the sub fields of mathematics overlap. Tools can be applied from linear algebra algebra analysis geometry topology and combina torics. In this book all of these fields make an appearance. Tiling theory provides an opportunity to demonstrate the interconnectedness of mathematics