Adaptive Array Signal Processing is concerned with the extraction of information from signals collected using an array of sensors. These signals propagate spatially through a medium, for example air or water, and the resulting wave front is sampled by the sensor array. Sensor arrays are found in a wide range of applications, including radar, sonar, seismology, biomedicine, communications, astronomy, and imaging. We will also discuss compressed sensing methods in the context of the massive amount of data being acquired by such lage (multi-sensor) systems.