Sensors and signal processing hardware and algorithms are under increasing pressure to accommodate ever larger and higher-dimensional data sets; ever faster capture, sampling, and processing rates; ever lower power consumption; communication over ever more difficult channels; and radically new sensing modalities. This four-hour course presents the fundamental theory and selected applications of Compressive Sensing, a new approach to data acquisition in which analog signals are digitized for processing not via uniform sampling but via inner products with random test functions. Unlike Nyquist-rate sampling, which completely describes a signal by exploiting its bandlimitedness, Compressive Sensing reduces the number of measurements required to completely describe a signal by exploiting its compressibility. The implications are promising for many applications and enable the design of new kinds of analog-to-digital converters, imaging systems and cameras, and radar systems, among others.