Derive relation between mass and energy

Question

how to derive the relativity relationo of mass energy $E=mc²$?
where can I found a very well explained derivation of this equation?

Answer 1

You'll find this derivation probably in every introductory textbook on special relativity. I especially recommend the Feynman lectures (chapter 15 "The Special theory of relativity", section 15-9 "Equivalence of mass and energy").
A short quote from there:

$$mc^2=m_0c^2+\frac12 m_0v^2+\cdots \tag{15.12}$$ Here, the term on the left expresses the total energy of a body, and we recognize the last term as the ordinary kinetic energy. Einstein interpreted the large constant term, $m_0c^2$, to be part of the total energy of the body, an intrinsic energy known as the “rest energy.”