Steffen,
Regarding the pedigree, Sky & Telescope's "Gleanings Bulletin C" provides all the early history including D.D. Maksutovs original paper, John Gregory's design and a few others. These articles cover the theory behind a prime-focus Maksutov (essentially a Maksutov-Newtonian), the familiar Maksutov Cassegrain, and the theory for the sub-aperture corrector as used by Vixen and a few others. I have a copy, if interested. Scientific American's 3-volume set "Amateur Telescope Making" from the 1950's has a few chapters too, mainly on making the corrector. Interesting reading.
There are some texts that cover the maksutov design.
As the Mak uses spherical surfaces to a first approximation, the design is analytic and the fundamentals of the corrector can be solved algebraically, see for example
http://www.cfht.hawaii.edu/~baril/Ma.../Maksutov.html
http://www.telescope-optics.net/maks...ctor_radii.htm
http://www.telescope-optics.net/maks..._telescope.htm
http://www.telescope-optics.net/Mak_spherical.htm
http://www.telescope-optics.net/MCT_off_axis.htm
After that, there are a few more variants such as the Field, van VenRooi, Rumak, Sigler and Rutten ones, which appear in ATM articles which appeared in Sky & Telescope as well as a few in a rather more serious journal "Applied Optics", for which you have to trawl the annual and 10 year indexes.
Of these the Rumak is perhaps the most interesting one as it was an attempt to produce a fast (f/8) design by separating the secondary from the corrector, although the central obstruction is of necessity quite large, though that won't matter to a camera.
The Questar, Meade and Skywatcher ones are basically the Gregory design.