There are many causes for mutations, but some of them are:
- soft mutation after a feminine noun (e.g. het wen "a white hate")
- soft mutation as a predicate after yn (e.g. Mae'n het yn wen "The hat is white" or Mae'n llyfr yn wyn "The book is white")
- soft mutation after possessive dy (e.g. dy wyn "your white", e.g. an egg white) or ei when it means "his" (e.g. ei wyn e "his white")
- aspirate mutation after possessive ei when it means "her" - no change in this case as g- does not change under aspirate mutation (e.g. ei gwyn hi "her white")
- nasal mutation after possessive fy (e.g. fy ngwyn "my white")
Some prepositions and conjunctions also cause certain mutations.
You'll discover them in due course :)
gwen is for modifying feminine nouns, but you will probably see that form most often as wen since adjectives after feminine nouns mutate softly.
gwyn is for modifying masculine nouns, and can also be a noun itself.
Welsh has no neuter gender.
The triggers for mutations that I mentioned are only some of the possible ones.
Some possessives do not trigger mutations.
The basic word is gwyn. You will sometimes see gwen being used after feminine nouns, mutated to wen. For example, het wen instead of het wyn, although het wyn is perfectly acceptable these days. Occasionally, you may even see the plural form gwynion being used - hetiau gwynion. Again, hetiau gwyn is perfectly acceptable.
Gwyn and Gwen are also used as first names.
Sometimes the plural forms are used as nouns in their own right, as in y Gleision (the Cardiff Blues - the name of a rugby team).
Mwyar duon (blackberries) shows another plural form, du -> duon.