Can anyone identify which suttas these quotes (having to do with the sense of self) come from? This document contains instructions for ridding the sense of a personal self. I was wondering which suttas (or other texts) the quotes at the end come from:


  “By rightly understanding ‘I am,’ one makes and end of suffering.”


and:


  “The eradication of ‘I am’ is the attainment of Nibbana here and now.”
I think the first one is for example the Kutuhalasala Sutta (SN 44.9) (S iv 398), the relevent sentence in that translation being:


  Instead, he describes him thus:
  
  
    "He has cut through craving, severed the fetter, and by rightly breaking through conceit has made an end of suffering &amp; stress."'
  


I think that "rightly breaking through conceit" might be a translation of of the same text as "rightly understanding ‘I am’" (because "breaking through" = "understanding", and "I am" = "conceit").

There's more about the relationship between "conceit" and "identity view" in the answers to this topic.

Another translation is here:


  But, he declares of him, thus:
  
  
    “He has cut off craving, and through full mastery over conceit, he has
    made a total end of suffering.”
  


This gives the Pali in a footnote:


  Acchejji taṇhaṁ vivattayi saññojanaṁ sammā,mānâbhisamayā antam akāsi dukkhassâ ti.


Here's part of a dictionary definition of one of those words, Abhisamaya


  Abhisamaya, (abhi + samaya, from sam + i, cp. abhisameti &amp; sameti; BSk. abhisamaya, e. g. Divy 200, 654) “coming by completely”, insight into, comprehension, realization, clear understanding, grasp, penetration.


So you can see how that word might be translated as "understanding" and/or "penetration".

A later part of that same dictionary definition says,


  sammā-mān’âbhisamaya full understanding of false pride in ster. phrase "acchecchi (for acchejji) taṇhaṃ, vivattayi saññojanaṃ sammāmānâbhisamayā antam akāsi dukkhassa" at S.IV, 205, 207, 399; A.III, 246, 444; It.47


... in other words:


It's a "ster. phrase" (maybe "stereotypical phrase"?)
That dictionary translates it as "full understanding of false pride"
It can be found in several suttas, including S.IV (205, 207, and 399), A.III (246 and 444), and It.47.


And indeed, as stated in that definition, here it is again at the end of (for example) the Nissaraniya Sutta (AN 5.200) (A iii 245):


  He has cut through craving, has turned away from the fetter, and by rightly breaking through conceit he has put an end to suffering &amp; stress.


So it's found in at least two of the suttas (quoted/hyperlinked above), and presumably found in at least all 6 of the suttas referenced in the dictionary definition above.