The theories of V. V. Wagner (1908-1981) on abstractions of systems of binary relations are presented here within their historical and mathematical contexts.  This book contains the first translation from Russian into English of a selection of Wagner’s papers, the ideas of which are connected to present-day mathematical research.  Along with a translation of Wagner’s main work in this area,  his 1953 paper ‘Theory of generalised heaps and generalised groups,’ the book also includes translations of three short precursor articles that provide additional context for his major work. Researchers and students interested in both algebra (in particular, heaps, semiheaps, generalised heaps, semigroups, and groups) and differential geometry will benefit from the techniques offered by these translations, owing to the natural connections between generalised heaps and generalised groups, and the role played by these concepts in differential geometry.  This book gives examples from present-day mathematics where ideas related to Wagner’s have found fruitful applications.