In addition to what you can glean from replies here, see if your local library can interlibrary loan a copy of Frank de Haas' OOP book Single Shot Rifles and Actions and its sequel, More Single Shot Rifles and Actions:
https://www.amazon.com/Single-Shot-Rifles-Actions-Frank/dp/B0007F3P9G
https://www.amazon.com/More-Single-...ore+single+shot&qid=1581146086&s=books&sr=1-1
There are other good books on the general subject, but de Haas is readable without getting overly technical and includes fairly good illustrations of the mechanisms.
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I like many kinds of rifles, but have an especial soft spot for single shot cartridge guns. They force me to slow down and savor every shot instead of rapidly burning through full magazines.
When it comes to currently available action types, the break open (called kipplauf in German-speaking countries), falling and rolling blocks are most common today.
You can find economy (sub-$500) break actions from makers such as Bergara/CVA and Henry (or a used H&R/NEF), or spend thousands on a fine example of German, Austrian or Italian make. Thompson/Center offers rifle and carbine configurations for their Contender and Encore single shot pistol that run somewhere in the $6-700 range.
Here's three of my H&R Handi Rifles with a couple of extra barrels:
View attachment 890312
https://cva.com/product-line/hunter/
https://www.henryusa.com/rifles/single-shot-rifle/
My Encore in .22 K Hornet (I've since swapped a pair of lower rings):
View attachment 890311
https://www.tcarms.com/firearms/interchangeable-platforms
Here's an example of fine Heym Kipplauf (not mine -- I wish!) that will set you back quite a few grand:
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The Ruger No.1 and the Italian Sharps and Winchester copies are the current entry level for new falling block rifles, starting somewhere north of one grand and up. Here's my pair of Rugers:
View attachment 890313
https://ruger.com/products/no1/models.html
https://www.uberti-usa.com/cartridge-rifles
https://www.davide-pedersoli.com/guns-rifles.asp/l_en/partenza_0/idl_2/rifles/rifles.html
C Sharps offers USA-made quality repros of Winchester and Sharps for a bit more, starting prices close to two grand:
http://csharpsarms.com/index.php. I could be wrong, but except for Tippmann's version the Rollingblock market is limited to the Italians right now. The Tippmann's go for just under on grand:
https://tippmannarmory.com/shop-all/
Then there's the antique market, where variety and price are all over the place. I won't even go there -- read de Haas or Grant for an education on the good old stuff. Personally, I like the Peabody-Martini action type (often called a tilting block) and own a couple of reworked British Martini military and cadet actions:
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