Systems composed of interacting autonomous agents offer a promising software engineering approach for developing applications in complex domains. However, this multiagent system paradigm introduces a number of new abstractions and design/development issues when compared with more traditional approaches to software development. Accordingly, new analysis and design methodologies, as well as new tools, are needed to effectively engineer such systems. Against this background, the contribution of this article is twofold. First, we synthesize and clarify the key abstractions of agent-based computing as they pertain to agent-oriented software engineering. In particular, we argue that a multiagent system can naturally be viewed and architected as a computational organization, and we identify the appropriate organizational abstractions that are central to the analysis and design of such systems. Second, we detail and extend the Gaia methodology for the analysis and design of multiagent systems. Gaia exploits the aforementioned organizational abstractions to provide clear guidelines for the analysis and design of complex and open software systems. Two representative case studies are introduced to exemplify Gaia's concepts and to show its use and effectiveness in different types of multiagent system.