  We explore the design of a space mission, Project Lyman, which has the goal
of quantifying the ionization history of the universe from the present epoch to
a redshift of z ~ 3. Observations from WMAP and SDSS show that before a
redshift of z >~ 6 the first collapsed objects, possibly dwarf galaxies,
emitted Lyman continuum (LyC) radiation shortward of 912 A, reionizing most of
the universe. How LyC escapes from galactic environments, whether it induces
positive or negative feedback on the local and global collapse of structures,
and the role played by clumping, molecules, metallicity and dust are major
unanswered theoretical questions, requiring observational constraint. Numerous
intervening Lyman limit systems, which frustrate the detection of LyC from high
z objects, thin below z ~ 3 where there are a few objects with apparently very
high fesc. At low z there are only controversial detections and a handful of
upper limits. A wide-field multi-object spectroscopic survey with moderate
spectral and spatial resolution can quantify fesc within diverse spatially
resolved galactic environments over redshifts with significant evolution in
galaxy assemblage and quasar activity. It can also calibrate LyC escape against
Ly-alpha escape, providing an essential tool to JWST for probing the beginnings
of reionization. We present calculations showing the evolution of the
characteristic apparent magnitude of star-forming galaxy luminosity functions
at 900 A, as a function of redshift and assumed escape fraction to determine
the required aperture for detecting LyC. We review our efforts to build a
pathfinding dual order multi-object spectro/telescope with a (0.5deg)^2
field-of-view, using a GSFC microshutter array, and crossed delay-line
micro-channel plate detector.
