THIS PROPOSED WORK AIMS TO LEARN MORE ABOUT THE COSMIC DAWN THE TIME WHEN THE UNIVERSE WAS HUNDREDS OF MILLIONS OF YEARS TO ONE BILLION YEARS OLD. THE COSMIC DAWN MARKS THE PERIOD WHEN THE FIRST STARS AND LATER GALAXIES TURNED ON. DESPITE ITS COSMOLOGICAL IMPORTANCE LITTLE IS DEFINITIVELY KNOWN ABOUT THESE TIMES. THE PROPOSED WORK WILL VASTLY IMPROVE MODELS FOR TWO OF THE MOST PROMISING COSMIC DAWN OBSERVABLES LYMAN-ALPHA IN EMISSION AND IN ABSORPTION AND IT IS RELEVANT FOR EXISTING UPCOMING AND PROPOSED NASA OBSERVATORIES SUCH AS HST JWST CIBER SPHEREX AND WFIRST. THERE IS A GROWING DATA SET OF Z = 5-7 LYMAN-ALPHA FOREST ABSORPTION SPECTRA (THE SO-CALLED LYMAN-ALPHA FOREST) AND THIS DATA SET IS SURE TO INCREASE AS HSC DES LSST WFIRST AND EUCLID LOCATE MORE HIGH-REDSHIFT QUASARS. EXISTING HIGH-REDSHIFT LYMANALPHA FOREST SPECTRA SHOW GUNN-PETERSON TROUGHS OF COMPLETE ABSORPTION AT Z~6 WHICH SUGGEST THAT THE PROPERTIES OF THE IGM ARE TRANSITIONING AROUND THIS REDSHIFT. HOWEVER THERE HAS ONLY BEEN A MODEST AMOUNT OF WORK AT MODELING THE HIGH-REDSHIFT LYMAN-ALPHA FOREST (IN PART BECAUSE OF THE LARGE COMPUTATIONAL DEMANDS) DESPITE THE FACT THAT WE HAVE YET TO UNDERSTAND WHAT THESE GUNN-PETERSON TROUGHS TRULY INDICATE. IN OUR ASSESSMENT THE MOST PROMISING AVENUE FOR SUBSTANTIAL NEAR-TERM PROGRESS IN OUR UNDERSTANDING OF COSMOLOGICAL REIONIZATION LIES IN DEVELOPING A MORE COMPREHENSIVE UNDERSTANDING OF THE Z=5-7 HI LYMAN-ALPHA FOREST. WE PROPOSE TO VASTLY IMPROVE MODELS OF THE Z=5-7 HI LYMAN-ALPHA FOREST. IN PARTICULAR WE WILL INCORPORATE MODELS FOR THE INHOMOGENEOUS RADIATION IONIZATION AND TEMPERATURE FIELD (ALL POSSIBLE SOURCES OF OPACITY FLUCTUATIONS) ON TOP OF TENS OF BILLION ELEMENT HYDRO-PM SIMULATIONS. THIS PROPOSAL ALSO CONCENTRATES ON THE LYMAN-ALPHA LINE IN EMISSION. WHILE LYMAN-ALPHA ABSORPTION IS SATURATING AT Z>~6 THIS EMISSION LINE IS UBIQUITOUS AS IT IS THE MAIN COOLANT OF PRIMORDIAL PHOTOIONIZED GAS AND POTENTIALLY CAN BE OBSERVED AT Z>~ 10. LYMANALPHA EMISSION FROM REIONIZATION-ERA GALAXIES HAS BEEN STUDIED THEORETICALLY IN QUITE A BIT OF DETAIL. HOWEVER GALACTIC LYMAN-ALPHA EMISSION IS OBSERVED TO BE FALLING OFF RAPIDLY WITH REDSHIFT ABOVE Z=6 WITH ALMOST NO EMISSION DETECTED AT Z=8. A FALL OFF IS EXPECTED ONCE THE HII REGIONS DURING REIONIZATION BECOME SMALLER THAN ~ 10 COMOVING MPC AS ALL THIS EMISSION WOULD BE SCATTERED BY THE NEUTRAL IGM. THE OBSERVED FALLOFF SUGGESTS THAT AT Z>~ 8 THE VAST MAJORITY OF LYMAN-ALPHA EMISSION SHOULD BE SCATTERED AND HENCE DIFFUSE. THIS DIFFUSE EMISSION IS POTENTIALLY DETECTABLE ALTHOUGH DISCERNING IT FROM FOREGROUNDS IS LIKELY TO BE A CHALLENGE. WE PROPOSE TO DEVELOP METHODS TO ISOLATE Z>6 DIFFUSE LYMAN-ALPHA EMISSION FROM FOREGROUND LINE EMISSION AS MUST BE DONE TO DETECT THIS SIGNAL. WE ARGUE THAT A FEW POSSIBILITIES MAY EXIST THAT USE THE DISTINCTIVE RADIATIVE TRANSFER PROPERTIES OF LYMAN-ALPHA IN A SIGNIFICANTLY NEUTRAL IGM. IN PARTICULAR THE SCATTERING OF LYMAN-ALPHA BY A NEUTRAL IGM BROADENS AND SHIFTS THE LINE BY ~10^3 KM/S IT POLARIZES THE EMISSION AND THE NATURE OF COSMOLOGICAL IONIZATION FRONTS SHOULD RESULT IN A DISTINCTIVE LINE PROFILE. WE WILL CREATE MAPS USING A MONTE-CARLO RADIATIVE TRANSFER ALGORITHM ON TOP OF REIONIZATION SIMULATIONS TO UNDERSTAND HOW THESE EFFECTS ARE ENCODED IN THE SIGNAL AND WHETHER THEY CAN BE USED TO ISOLATE IT FROM FOREGROUNDS.