The contemporary scientific method is built on reductionism. The surprising finding that this paradigm has limits gave rise to the concept of complexity. This book presents the new science of complexity by presenting diverse concepts from the analyses of a wide range of real world systems (chemical, biochemical, biological, and ecological). Based on a variety of approaches ranging from cellular automata and dynamic evolutionary networks to topology and information theory, the book contains methodologies of practical importance for assessing systems complexity and network analysis in medicine and biology. The techniques presented can be applied for comparative studies in proteomics and genomics, in the search for drugs and markers for early diagnostics, in clinical proteomics, in stability/fragility analysis of ecosystems, as well as for such analysis of fullerenes and other nanotechnology products. The volume combines original results of the authors, which are internationally recognized experts, with a broad coverage of this explosively developing area.