THE ULTIMATE EXPRESSION OF STRONG GRAVITY IN THE UNIVERSE IS A BLACK HOLE A REGION OF SPACETIME FROM WHICH NOTHING NOT EVEN LIGHT CAN ESCAPE. HIDDEN FROM OUR DIRECT VIEW BY THEIR VERY NATURE BLACK HOLES ARE ONLY ``SEEN" BY THEIR INTERACTION WITH A LIGHT-PRODUCING ENVIRONMENT. TWO BLACK HOLES MERGING TOGETHER LIGHT UP THE COSMOS IN GRAVITATIONAL WAVES WHILE REMAINING COMPLETELY DARK IN ELECTROMAGNETIC LIGHT. ON SEPTEMBER 14 2015 SUCH A CATACLYSMIC COLLISION WAS OBSERVED FOR THE FIRST TIME WHEN LIGO DETECTED THE GRAVITATIONAL WAVES EMITTED BY TWO BLACK HOLES MERGING CALLED GW150914. GRAVITATIONAL WAVES OR RIPPLES IN SPACETIME ARE THE ONLY MEANS TO DETECT BLACK HOLES DIRECTLY. LISA WILL OFFER UNPRECEDENTED VIEWS OF BLACK HOLES DETECTING GRAVITATIONAL WAVES FROM BLACK HOLE BINARIES ACROSS MULTIPLE MASS SCALES AND DEEP INTO THE HISTORY OF THE UNIVERSE INACCESSIBLE BY GROUND BASED DETECTORS LIKE LIGO. THIS PROPOSAL PREPARES FOR SUCH DETECTIONS BY PROVIDING THEORETICAL PREDICTIONS OF BLACK HOLES AT MULTIPLE MASS SCALES. THE CENTRAL THESIS OF THE PROPOSAL IS THE DETERMINATION OF THE SIGNATURE OF BLACK HOLE BINARIES OF UNEQUAL MASS RATIO IN WHICH ONE OF THE BLACK HOLES IS A HUNDRED OR MORE TIMES THE MASS OF ITS COMPANION. THESE SOURCES ARE EXPECTED TO BE RELATIVELY COMMON AND CURRENT METHODS FAIL TO CAPTURE THIS LIKELY LISA SOURCE. THE THEORETICAL FOUNDATION OF BLACK HOLE MERGERS AND THEIR GENERATION OF GRAVITATIONAL WAVES IS EINSTEIN'S THEORY OF GENERAL RELATIVITY. THERE ARE SEVERAL METHODS TO PRODUCE ACCURATE GRAVITATIONAL WAVEFORMS FOR THE COALESCENCE OF BLACK HOLE BINARIES. THIS WORK WILL REQUIRE KNOWLEDGE OF THESE APPROACHES AND NEW ONES. NUMERICAL RELATIVITY PROVIDES A MEANS TO SOLVE EINSTEIN'S EQUATIONS DURING THE NONLINEAR REGIME WHEN THE TWO BLACK HOLES MERGE. WHILE ADVANCES IN NUMERICAL RELATIVITY OVER THE LAST 13 YEARS HAVE BEEN MONUMENTAL AS OF YET NUMERICAL RELATIVITY CANNOT SOLVE SYSTEMS OF BLACK HOLES WITH MASS RATIOS MORE DISPARATE THAN ABOUT ONE TO ONE HUNDRED. FOR SYSTEMS WITH VASTLY DIFFERENT BLACK-HOLE MASSES CALLED EXTREME MASS RATIO INSPIRALS PERTURBATION THEORY PROVIDES SOLUTIONS. UNFORTUNATELY PERTURBATION THEORY IS BEST SUITED FOR MASS RATIOS IN THE THOUSANDS OR MORE RATHER THAN HUNDREDS. WHEN THE BLACK HOLES ARE EFFECTIVELY POINT MASSES MOVING AT A FRACTION OF THE SPEED OF LIGHT AN APPROXIMATION TO EINSTEIN'S THEORY KNOWN AS POST- NEWTONIAN PROVIDES THE ANSWER. ALL OF THESE APPROACHES WILL BE IMPORTANT IN THE BINARY BLACK HOLE LANDSCAPE OF LISA. BLACK-HOLE BINARIES OF MODERATE MASS RATIOS IN THE HUNDREDS WILL REQUIRE PUSHING THE BOUNDARIES OF NUMERICAL RELATIVITY AND PERTURBATION THEORY IN ORDER TO PROVIDE REASONABLE SOLUTIONS FOR WHICH NEITHER APPROACH CAN DO ALONE. SEVERAL OF THE DRIVING SCIENTIFIC OBJECTIVES FOR LISA WILL DEPEND ON SUCCESSFUL STUDIES LIKE THAT PROPOSED. LISA IS TO ``TRACE THE ORIGIN GROWTH AND MERGER HISTORY OF MASSIVE BLACK HOLES ACROSS COSMIC AGES" AND ``TO EXPLORE THE FUNDAMENTAL NATURE OF GRAVITY AND BLACK HOLES" TO NAME JUST TWO OBJECTIVES FROM THE LISA MISSION PROPOSAL. OUR WORK WILL CONTRIBUTE TO THIS GOAL AND THAT OF THE OVERALL MISSION OF NASA TO PROBE THE COSMOS BY PROVIDING THE THEORETICAL FOUNDATIONS NECESSARY TO INTERPRET GRAVITATIONAL WAVE DETECTIONS IN TERMS OF THEIR ASTROPHYSICAL ORIGINS PROVIDING A MAP OF THE GRAVITATIONAL WAVES OF BINARY BLACK HOLES OF UNEQUAL-MASS. THERE ARE SEVERAL PRODUCTS THIS PROPOSAL WILL PRODUCE FOR LISA SCIENCE IF FUNDED. THE MAIN PRODUCT WILL BE WAVEFORMS OF BLACK-HOLE MERGERS WITH MASS RATIOS IN THE HUNDREDS. THESE WAVEFORMS WILL BE PROVIDED TO THE LISA MOCK DATA CHALLENGES TO STRESS TEST THE COMMUNITY'S ABILITY TO DETECT AND INTERPRET GRAVITATIONAL WAVES FROM THESE SYSTEMS. THE PROPOSED WORK WILL ALSO PRODUCE PAPERS AND NUMERICAL ALGORITHMS THAT PROVIDE GUIDANCE AND INSIGHT INTO GRAVITATIONAL WAVES FROM MODERATE MASS RATIO BLACK HOLE BINARIES AND THEIR INTERPRETATION.