Rather than the ordinary axiomatic approach to establish advanced quantum mechanics and badic quantum field theory upon postulates, in chapter 1 author introduces the 52 theorems, 16 corollaries, one criterion, and one law in "Quantum Mechanics upon Theorems", and prove two new theorems (Big theorem of energy and big theorem of wavepacket). In the other 9 chapters, this textbook proves 20 new theorems and 7 corollaries. For example, the commutation relations between field and field momentum are given by a theorem, and a convenient method to treat field quantisation of constrained system is given by a corollary.