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What you’re after is a book called “Unusual Telescopes” by Peter Manly which is mainly about unusual mountings.
In essence:
Refractors - Conventional singlet (monochromatic solar telescopes), achromatic doublets, apochromatic, aplanatic, Petzval, Dialyte, Schupmann just to name a few.
Reflectors - start with Newtonian, cassegrain, Gregorian, schmidt-cassegrain, maksutov cassegrain, Ritchey-Chretien. several variants of the maksutov, several variants with sub-aperture correctors ... then there’s the Loveday folded newtonian... a few three-mirror reflectors ...
Off axis types - the herschelian, two or three mirror schiefspieglers...
Then photographic exotics like the Wynne, Ricardi-Honders, Baker-Nunn...
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