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The authors of this book are scienti_c workers in the _eld of complex networks. This is an explosively developing multidisciplinary area, which involves practically everything, natural and arti_cial, in the world, and we, theoretical physicists, explore it, armed with the standard tools of statistical physics. What we are doing is uncovering the actual simplicity and beauty of complex systems including the random complex networks. The book is about the key ideas and concepts of this _eld which is already called the science of networks. The highly heterogeneous networked systems, which we explore, typically have no governing authority, no command centre taking decisions and issuing orders. Nonetheless, even without orchestration, these remarkably widespread systems function very e_ectively and reliably. Moreover, the absence of centralization in favour of distributed self-organization is vital for their existence and robustness.