Flares of known astronomical sources and new transient phenomena occur on different timescales, from sub-seconds to several days or weeks. The discovery potential of both serendipitous observations and multi-messenger and multi-wavelength follow-up observations could be maximized with a tool which allows for quickly acquiring an overview over both persistent sources as well as transient events in the relevant phase space. We here present COincidence LIBrary for Real-time Inquiry (Astro-COLIBRI), a novel and comprehensive tool for this task. Astro-COLIBRIs architecture comprises a RESTful API, a real-time database, a cloud-based alert system and a website (https://astro-colibri.com) as well as apps for iOS and Android as clients for users. The structure of Astro-COLIBRI is optimized for performance and reliability and exploits concepts such as multi-index database queries, a global content delivery network (CDN), and direct data streams from the database to the clients. Astro-COLIBRI evaluates incoming VOEvent messages of astronomical observations in real time, filters them by user-specified criteria and puts them into their MWL and MM context. The clients provide a graphical representation with an easy to grasp summary of the relevant data to allow for the fast identification of interesting phenomena and provides an assessment of observing conditions at a large selection of observatories around the world. We here summarize the key features of Astro-COLIBRI, the architecture and used data resources. We specifically provide examples for applications and use cases. Focussing on the high-energy domain, we showcase how Astro-COLIBRI facilitates the search for high-energy gamma-ray counterparts to high-energy neutrinos and scheduling of follow-up observations of a large variety of transient phenomena like gamma-ray bursts, gravitational waves, TDEs, FRBs, and others.
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