THE NONLINEAR OPTICS OF PLASMAS (NLOP) FOR BOTH LONG AND SHORT LASER PULSES IS FULL OF APPLIED AND FUNDAMENTAL RESEARCH TOPICS. RESEARCH IN NLOP FOR OVER FIFTY YEARS HAS STUDIED HOW LASERS INCIDENT ON A TENUOUS PLASMA CAN UNDERGO MANY NONLINEAR PROCESSES THAT GENERATE SCATTERED LIGHT AT DIFFERENT WAVELENGTHS THAN THE PUMP, DRIVE COLLECTIVE PLASMA MODES/OSCILLATIONS, AND INDIRECTLY ACCELERATE PARTICLES VIA THESE PLASMA MODES. OVER THE PAST SEVERAL YEARS, THERE HAS BEEN TREMENDOUS PROGRESS ON HOW TO SPATIALLY AND TEMPORALLY STRUCTURE LASER PULSES. THIS INCLUDES LASER PULSES WHERE THE PEAK INTENSITY LOCATION MOVES AT SUPERLUMINAL OR SUBLUMINAL SPEEDS (FASTER OR SLOWER THAN THE SPEED OF LIGHT) IN VACUUM (A FLYING FOCUS), WHERE THE PHASE FRONTS HAVE CORKSCREW SHAPES (ORBITAL ANGULAR MOMENTUM), AND WHERE THE POLARIZATION DIRECTION OF THE LASER VARIES WITHIN THE PHASE FRONT OF THE LASER. THE VACUUM PROPAGATION PROPERTIES OF THESE LASERS ARE WELL UNDERSTOOD, BUT THEIR INTERACTION WITH PLASMAS IS ONLY BEGINNING TO BE UNDERSTOOD AND APPRECIATED. FURTHERMORE, THE INTERACTION OF THESE SPATIALLY AND TEMPORALLY STRUCTURED LASER PULSES WITH PLASMAS IS MUCH DIFFERENT THAN THE INTERACTION OF MORE CONVENTIONAL LASERS WITH PLASMAS THAT HAS PRIMARILY BEEN STUDIED TO DATE. THIS WORK IS RAPIDLY OPENING UP NEW RESEARCH TOPICS IN THE NONLINEAR OPTICS OF PLASMAS. UCLA PROPOSES A THEORETICAL AND COMPUTATIONAL EFFORT WITH THE OBJECTIVE TO LAY THE FOUNDATION FOR UNDERSTANDING SUCH INTERACTIONS AS WELL AS TO DEVELOP NEAR-TERM APPLICATIONS. THE RESEARCH WILL BE DISCOVERY-DRIVEN BUT WITH AN EYE TOWARDS IMPACTING SEVERAL APPLIED AREAS. IT IS ANTICIPATED THIS EFFORT WILL LEAD TO A DECADAL LONG EFFORT.