Note: You can write an answer from the perspective of one or more schools, whichever you know best and also I read somewhere that some schools consider Mahavakyas as quoted out of the context, if you think so you can quote the whole verse to provide the context you intend for your interpretation.
In this question I read about much controversial alleged debate between Shri Vidyaranya and Shri Akshobhya Tirtha.
And it was really curious that the debate was over the meaning of Mahavakya Tat Tvam Asi (तत् त्वम् असि). Source
So I wanted to know what are the exact interpretations of the four main Mahavakyas from all the three schools of Vedanta.
1. Prajnanam Brahma (प्रज्ञानम् ब्रह्म)
2. Aham Brahma Asmi (अहम् ब्रह्म अस्मि)
3. Tat Tvam Asi (तत् त्वम् असि)
4. Ayam Atma Brahma (अयम् आत्मा ब्रह्म)