The present monograph is a revised and extended version of my PhD thesis submitted to and defended at the Department of Mathematics, Dresden University of Technology, 2000. First of all, I would like to thank my supervisor, Manfred Droste. His questions on the topology of Mazurkiewicz traces marked the starting point of my research. I am very grateful for his guidance and his perpetual interest. Several people assisted me with my research. In particular, I owe many thanks to Dietrich Kuske. I benefited a lot from the stimulating discussions with him. After all, they have led to the characterization of the topology of real traces in Chapter 6. I am also indebted to Achim Jung. His suggestion to extend the notion of a "pop" has culminated in a separate chapter (Chapter 2). With their invaluable suggestions, the referees of my PhD thesis-Manfred Droste, Achim Jung, and Ralph Kopperman-helped improve this monograph a lot. I greatly acknowledge the support of the PhD programme "Specification of discrete processes and systems of processes by operational models and logics" (Department of Computer Science) as well as the pleasant atmosphere at the Institute of Algebra (Department of Mathematics) at Dresden University of Technology. Finally, I wish to thank Szisza Zvada for her emotional support and encouragement.