The science of forgiveness:  "I am sorry, and you also please forgive me".

• By practicing prāyaschitta (repentance), a soul gets rid of sins, and commits no transgressions; he who correctly practices prāyaschitta gains the road and the reward of the road, he wins the reward of good conduct. By begging forgiveness he obtains happiness of mind; thereby he acquires a kind disposition towards all kinds of living beings; by this kind disposition he obtains purity of character and freedom from fear.   -- [This is essence of the Jain Pratikraman. Here is a link with perfect pronunciations of the Pratikraman.

• Please click on this link for Pratikraman audio  / video  http://www.herenow4u.net/index.php?id=81053

• Māhavīra in Uttarādhyayana Sūtra 29:17–18.  In Jainism, forgiveness is one of the main virtues that need to be cultivated by the Jains. Ksamāpanā or supreme forgiveness forms part of one of the ten characteristics of dharma.  In the Jain prayer, (Pratikraman) Jains repeatedly seek forgiveness from various creatures—even from ekindriyas or single sensed beings like plants and microorganisms that they may have harmed while eating and doing routine activities.   Forgiveness is asked by uttering the phrase, Micchāmi dukkaḍaṃ. Micchāmi dukkaḍaṃ is a Prakrit language phrase literally meaning "may all the evil that has been done be fruitless."   During Samvatsari — the last day of Jain festival paryusana —Jains utter the phrase Micchāmi dukkaḍaṃ after Pratikraman. As a matter of ritual, they personally greet their friends and relatives Micchāmi dukkaḍaṃ  seeking their forgiveness. No private quarrel or dispute may be carried beyond Samvatsari, and letters and telephone calls are made to the outstation friends and relatives asking their forgiveness.  

• Pratikraman also contains the following prayer:  Khāmemi savva - jīve savvë jive khamantu me / metti me savva - bhūesu, veram mejjha na kenavi //

(I ask pardon of all creatures, may all creatures pardon me.  May I have friendship with all beings and enmity with none.)

• In their daily prayers and samayika, Jains recite Iryavahi sutra seeking forgiveness from all creatures while involved in routine activities.