"Looking up on a starry night, it’s easy to imagine that the Universe is unchanging. In reality, however, the Universe is teeming with activity: there are massive explosions from accreting black holes, bright radio flashes from ultra-magnetic pulsars, and likely other spectacles that have so far escaped our prying eyes. These fleeting events can happen faster than the blink of an eye and, importantly, they trace the most extreme astrophysical phenomena. Catching these rare performances poses a major challenge for observational astronomers, but the scientific payoff is well worth the effort.With this proposal, I will mould the Low-Frequency Array (LOFAR) telescope into DRAGNET, the world's premier high-speed, wide-angle camera for radio astronomy. Radio waves are a unique and powerful way of investigating the most extreme astrophysical processes. With DRAGNET I will characterize the rate of fast radio transients, i.e. astrophysical bursts lasting less than a second, and search for new astrophysical phenomena in this largely unexplored domain. This has the potential to give us transformative insight into the extremes of gravity and dense matter. Alongside this, I will simultaneously monitor hundreds of radio-emitting neutron stars (pulsars) on a regular basis. This will allow me to understand why some neutron stars pulse regularly, while others show rapid switches in their emission properties. This will address the physics behind the strongest magnetic fields in the Universe.I have led the construction of LOFAR's high-time-resolution observing capabilities; in this project I will capitalize on that investment and do cutting-edge science that is beyond the reach of any other existing telescope. Simply put, this project will establish a world-leading research group in the emerging field of fast radio transients and will crystallize the wide-field radio telescope as an essential tool for unveiling the bustling activity that makes our Universe so interesting to study."