Mac Mail v. 7.1 (1827) spell checker makes spelling suggestions that are MISSPELLED!

Question

I haven't been able to find this anywhere on the web so far, so thought I would post it here. 
I am running Mavericks (v10.9.1) on a Mac Book Pro 17" (Early 2011).  
When typing in Mac Mail (or Pages, etc.), my auto-spell check frequently makes suggestions that are misspelled.  For example, I typed "availabillty", and the auto-checker suggested "AVAILABILTY"(!?!).  The correct spelling, of course, being AVAILABILITY. 
This has happened several times before, and I just didn't document any of the other misspellings.  I will add others, if that makes a difference. 
I've tried to find access to the library to make corrections to the internal misspellings, but cannot seem to find and assuming not accessible?? 
Please help!  This is an incredibly annoying problem, making the spell-checking functionality essentially worthless having to stop and "spell-check the spell-checker" everytime.

Answer 1

Pedro,
Thanks, I apprecaite the info, but you did not address my question.  The links you provided just explained the basics of spell-checking and how to do things like "learn new words".  The do not provide any "information regarding what I'm trying to accomplish". 
Perhaps I didn't explain my problem clearly enough:  My problem is there are INCORRECT suggestions being made by the Apple spell-checker (or whatever library it's using).  In other words, I'm spelling a word correctly, and the auto-spell-checker is suggesting incorrect spellings to my correctly spelled word.     
What I'm trying to accomplish is getting misspelled words out of the auto-correction library (and also figure out how they got in there in the first place).  Is there a way to edit the existing words in the spell-checking library (not just adding new ones, as the link you provided pointed out).
Thanks,
Dan