The Department of Complexity Science and Engineering was established with the aim of investigating various problems related to complexity through an integrated approach, combining the science of complexity and the engineering of complexity, and training scientists and engineers who can create new paradigms of complexity science and engineering. Modern science has achieved great success in understanding a complex system on the basis of reductionism, by first decomposing it into constituent elements, elucidating their properties and functions, and finally reconstructing the whole system by superimposing these elements. This methodology is basically supported by the strong belief of modern science that Nature is governed by simple rules and the clarification of these rules is precisely the aim of science. Moreover, such a reductionistic approach has been linked strongly with the beautiful system of linear theory, which is another giant pillar that supports the present science and engineering. This is because in linear theory, "the principle of superposition" holds, in other words, the sum of solutions is also a solution. However, we are now confronted with realities in which a variety of complex nonlinear phenomena, which are irreducible into simple rules, surely exist in both natural and artificial systems. Furthermore, triggered by the emergence of new nonlinear concepts such as chaos and fractal, it is becoming increasingly obvious that dynamically and computationally complex systems, in which linear approximation is never useful any more and various nonlinear elements interact strongly with each other, are ubiquitous in this real world and studies of such complex systems have substantial meanings in science and engineering. In fact, it is widely expected that understanding complex systems in the real world can create new science and engineering of the 21st century, surmounting simple alternative confrontations, like deterministic theory against probability theory, necessity against coincidence, the whole against the parts, universality against variety, subjective against objective, and mechanism against teleology. The Department of Complexity Science and Engineering is based on harmonizing science and engineering with the aim of creating the new discipline of complexity science and engineering. Now, we have started tackling essentially important but really difficult problems of complexity science and engineering using two main approaches, namely (1) experimental and observational approaches on real-world complex systems such as the plasma, strongly correlated electrons, solid-surface, the earth and the planets, the brain, and the genome, and (2) theoretical approaches using nonlinear modeling, deterministic chaos, system control, large-scale computation, data mining, and computer graphics. Through mutual interaction between experimental-observational approaches and theoretical ones and repetition of analysis and synthesis, the Department of Complexity Science and Engineering challenges the science and engineering of complexity from a transdisciplinary viewpoint .