The KI ´09 workshop on Complex Cognition was a joint venture of the Cognition group of the Special Interest Group Artificial Intelligence of the German Computer Science Society (Gesellschaft für Informatik) and the German Cognitive Science Association. Dealing with complexity has become one of the great challenges for modern information societies. To reason and decide, plan and act in complex domains is no longer limited to highly specialized professionals in restricted areas such as medical diagnosis, controlling technical processes, or serious game playing. Complexity has reached everyday life and affects people in such mundane activities as buying a train ticket, investing money, or connecting a home desktop to the internet. Research in cognitive AI can contribute to supporting people navigating through the jungle of everyday reasoning, decision making, planning and acting by providing intelligent support technology. Lessons learned from expert systems research of the nineteen-eighties show that the aim should not be to provide for fully automated systems which can solve specialized tasks autonomously but instead to develop interactive assistant systems where user and system work together by taking advantage of the respective strengths of human and machine. To accomplish a smooth collaboration between humans and intelligent systems, basic research in cognition is a necessary precondition. Insights into cognitive structures and processes underlying successful human reasoning and planning can provide suggestions for algorithm design. Even more important, insights into restrictions and typical errors and misconceptions of the cognitive systems provide information about those parts of a complex task from which the human should be relieved. For successful human-computer interaction in complex domains it has, furthermore, to be decided which information should be presented when, in what way, to the user. We strongly believe that symbolic approaches of AI and psychological research of higher cognition are at the core of success for the endeavor to create intelligent assistant system for complex domains. While insight into the neurological processes of the brain and into the realization of basic processes of perception, attention and senso-motoric coordination are important for the basic understanding of the principles of human intelligence, these processes have a much too fine granularity for the design and realization of interactive systems which must communicate with the user on knowledge level. If human system users are not to be incapacitated by a system, system decisions must be transparent for the user and the system must be able to provide explanations for the reasons of its proposals and recommendations. Therefore, even when some of the underlying algorithms are based on statistical or neuronal approaches, the top-level of such systems must be symbolical and rule-based. The papers presented at this workshop on complex cognition give an inspiring and promising overview of current work in the field which can provide first building stones for our endeavor to create knowledge level intelligent assistant systems for complex domains. The topics cover modelling basic cognitive processes, interfacing subsymbolic and symbolic representations, dealing with continuous time, Bayesian identification of problem solving strategies, linguistically inspired methods for assessing complex cognitive processes and complex domains such as recognition of sketches, predicting changes in stocks, spatial information processing, and coping with critical situations.