preface explaining the American edition’s practical aims, expanded content, modernized tooling, integrated illustrations, and thorough indexing. An extensive index outlines the breadth of topics, after which Part I begins by arguing that arithmetic, geometry, and drawing are essential foundations for competent watch repair and construction despite interchangeable manufacturing. It then offers concise refreshers on calculation signs, powers and roots (including square-root extraction), proportions, and the elements of practical geometry (circles, angles, plane areas, and volumes). The text proceeds to basic drawing practice and conventions, tracing and transferring methods, and key instruments (rules, protractor, scales, sector, proportional compass, vernier, micrometer screw), before introducing core geometric constructions for perpendiculars, parallels, subdivisions, and angle replication—ending mid-topic on subdividing an angle. (This is an automatically generated summary.)