that, in its selection of material and its formulation of geometry, the book "largely reflects work of C. Caratheodory and E. Cartan". Audience and reception Geometry of Complex Numbers is written for advanced undergraduates and its many exercises (called "examples") extend the material in its sections rather than merely checking what the reader has learned. Reviewing the original publication, A. W. Goodman and Howard Eves recommended its use as secondary reading for classes in complex analysis, and Goodman adds that "every expert in classical function theory should be familiar with this material". However, reviewer Donald Monk wonders whether the material of the book is too specialized to fit into any class, and has some minor complaints about details that could have been covered more elegantly. By the time of his 2015 review, Mark Hunacek wrote that "the book has a decidedly old-fashioned vibe" making it more difficult to read, and that the dated selection of topics made it unlikely to be usable as the main text for a course. Reviewer R. P. Burn shares Hunacek's concerns about readability, and also complains that Schwerdtfeger "consistently lets geometrical interpretation follow algebraic proof, rather than allowing geometry to play a motivating role". Nevertheless Hunacek repeats Goodman's and Eves's recommendation for its use "as supplemental reading in a course on complex analysis", and Burn concludes that "the republication is welcome". Related reading As background on the geometry covered in this book, reviewer R. P. Burn suggests two other books, Modern Geometry: The Straight Line and Circle by C. V. Durell, and Geometry: A Comprehensive Course by Daniel Pedoe. Other books using complex numbers for analytic geometry include Complex Numbers and Geometry by Liang-shin Hahn, or Complex Numbers from A to...Z by Titu Andreescu and Dorin Andrica. However, Geometry of Complex Numbers differs from these books in avoiding elementary constructions in Euclidean geometry and instead applying this approach to higher-level concepts such as circle inversion and non-Euclidean geometry. Another related book, one of a small number that treat the Möbius transformations in as much detail as Geometry of Complex Numbers does, is Visual Complex Analysis by Tristan Needham. References External links Geometry of Complex Numbers (1979 edition) at the Internet Archive Circles Inversive geometry Non-Euclidean geometry Mathematics textbooks 1962 non-fiction books 1979 non-fiction books