The book presents results of research on how students, future mathematics teachers, come to comprehend a piece of advanced mathematics, so called restricted arithmetic. In particular, it looks into the following questions: Do students use analogies from other familiar structures such as ordinary arithmetic? To what extent do students apply their knowledge from abstract algebra? How does the fact that students are working on their own piece of mathematics as opposed to being introduced to it in a transmissive way, affect their understanding? The practical goal peculiar to restricted arithmetic was to look for ways of re-learning (university mathematics) knowledge, previously acquired mechanically, with understanding. This book is aimed for professionals in mathematics education, young researchers and PhD students. We hope that they can not only learn something new about students and their learning of mathematics but also find an inspiration for their own research work.