Is there a comprehensive dictionary of abbreviations out there or, failing that, a document wherein one can find the accepted "rules" to abbreviate words in the English language?
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There's certainly no comprehensive dictionary of abbreviations, as any individual, company, or even fandom can easily have its own abbreviations on top of any standard ones. Wikipedia is probably your best bet for a somewhat complete list, but this will still be missing a lot of more specific abbreviations. For example, as of right now, DM is missing the definition "direct message", which is common in Discord chat rooms.
English uses many sorts of abbreviations (which are generally considered to include acronyms, etc., especially in common speech), and there really is no set rule to how to abbreviate. As such, most sources on "abbreviation rules" list how to use abbreviations rather than how to make them. Those that do tend to say "these are the categories" with no rules on how or when to apply each category.
So let me lay out the most common forms of abbreviation, based on both Oxford and personal experience:
However, which type of abbreviation is called for is decided entirely by the individual word, and many words have multiple abbreviations. On various calenders, for example, "Thursday" may be abbreviated "Thurs", "Thu", "Th", "T", or even "R" (to keep it straight from Tuesday). Not to mention, there are also words that use different sorts of abbreviations, too.
Overall, because abbreviations are not standardized, but rather created out of convenience, there really will never be a complete list of every abbreviation in English, nor comprehensive rules for how to make abbreviations.