The Lattice Assumption Zoo currently catalogues 71 assumptions; couting… counting non-trivial variants.

Tags Explained

standard tags mark assumptions that can be reduced to long-standing, open problems and have undergone significant cryptanalytic effort.
implied tags mark assumptions with a reduction from a standard assumption that does not impose unusually strict conditions on parameter choices.
broken tags mark assumptions that have been compromised by known attacks.

List of Catalogued Assumptions

LWE-Based Assumptions
SIS-Based Assumptions
Standalone Assumptions