When using in, 'nin or min, refer to the letter(s) before the slash in the chart above. When using an, dan, or athan, refer to the letter(s) after the slash. What this indicates is how the trigger word alters after the final vowel. That is, everything before the final vowel remains the same. If the letter before the slash is simply "i", that means that in mutates to i, 'nin mutates to 'ni, and min mutates to mi. Similarly, if the letters after the slash are "am", that means that an mutates to am, dan mutates to dam, and athan mutates to atham. For example:

the trees --> in + gelaidh --> i ngelaidh
against a friend --> dan + mellon --> dam mellon
beyond a forest --> athan + tawar --> atha thawar

mixed mutation

Mixed mutation occurs most often with prepositions that incorporate the definite article; that is, prepositions that include a "the" as part of their translation. The following is the list of words that cause mixed mutation:

When referring to the chart above, the letters in parentheses apply ONLY if you are using en; all other words in this group remain unchanged. Examples:

light of the forest --> calad + en + tawar --> calad-e-dawar
for the enemy --> 'nin + coth --> 'nin goth
under the knife --> nuin + sigil --> nuin higil

stop mutation

Stop mutation is caused by prepositions and prefixes that end in -t or -d. (This would presumably also apply to compound words where the first element ends in -t or -d, as well.) The list of triggers words is below:

Note that o becomes od when it precedes words that begin with vowels, which is why it triggers stop mutation. The letters in parentheses in the master mutation chart only apply if you are using ed or ned. Ad- and o remain unchanged. Examples:

out of clothing (undressed) --> ed + hammad --> e chammad
in Gondor --> ned + Gondor --> ne Gondor
from Mirkwood --> o + Taur-na-fuin --> o Thaur-na-fuin

liquid mutation

Tolkien never explicitly wrote about liquid mutation, but we can infer its existence from his other writings. Liquid mutation happens after prepositions and prefixes that end in -l or -r. Like stop mutation, we can see that this type of mutation also occurs in compound words where the first element ends in -l or -r. Liquid mutation is known to be caused by the following:

It is important to point out that there are two meanings of the prefix ar-. When used to mean "without", it causes liquid mutation, but when used to mean "royal, exalted", it causes lenition. None of these words alter their final consonants, which is why there are no parentheses for liquid mutation in the chart above. Examples:

above Caradhras --> or + Caradhras --> or Charadhras
without fear --> ar- + del --> ardhel
shadow (dark shape) --> mor + cant --> morchant

conclusion

• Nasal mutation is caused by in, 'nin (plural only), an, dan, and presumably min and athan.
• Mixed mutation is caused by en, 'nin (singular only), ben, erin, nan, nuin, and uin.
• Stop mutation is caused by ad-, ed, ned, and o.
• Liquid mutation is caused by or and ar- (when it means "without").
• Stop and liquid mutations can also occur in compound words.
• Mutations can cause alterations in the prepositions as wel as the words themselves. See the chart for details.
• Don't forget to check for special case vocabulary.