A few simple(?) points, specifically the first write-up suggests that there are many more hebrew letters than there are. While this point is embedded in the other write-ups, I for one was unable to understand them, and I imagine I wasn't the only one. So I've endeavored to clarify a few things.

There are either 22 or 27 hebrew letters, depending on how you look at it.

  1. There are the 22 basic letters.
  2. Within these 22 are 5 letters that are written/printed differently when they appear at the end of a word.
  3. There are 7 letters within the 22 which each have two different ways to be pronounced depending on their usage.
  4. Of these 7, only 4 are universally still pronounced both ways. Some ashkenazim pronounce 5 and some sepharadim pronounce 6. No one currently pronounces the 7th letter (ר), partially because it would rarely ever be pronounced the second way even if people knew how.
  5. There is an 8th letter (ש) which has two pronunciations (pronounced by everyone) but is not considered a double letter.

The 22 letters were listed above and they are: (asterisks mark the one's with dual pronunciation.)((a) denotes pronunciation by some ashkenazim) ((s) denotes pronunciation by some sepharadim) ((m) denotes pronunciation in modern hebrew)
א
ב *(a)(s)(m)
ג *(s)
ד *(s)
ה
ו
ז
ח
ט
י
כ *(a)(s)(m)
ל
מ
נ
ס
ע
פ *(a)(s)(m)
צ
ק
ר
ש (a)(s)(m) (i'm still researching)
ת *(a)(s)

sources: personal experience, the seventh dual-pronunciation letter is mentioned along with the others in the Sefer Yetzirah as well as in other Jewish sefarim.
please correct any errors