This weeks reading from Advanced Solid State Physics by Philip Phillips is Chapter 3, Second Quantization. Some key ideas:
Quasi-particles in quantum many-body theory are either fermions or bosons. The difference is seen in whether their creation and annihilation operators obey anti-commutation or commutation relations.
The second quantisation formalism provides a convenient and powerful book-keeping device to keep track of the fermionic (or bosonic) character of many-particle states.
A key result to become familiar with is writing a many-body Hamiltonian operator in second-quantised form, as in equation (3.33).
This is the starting point of Chapter 4, The Hartree-Fock approximation.
In the next chapter we will see how the anti-symmetric (fermionic) character of many-electron quantum states has an important physical consequence: the exchange interaction which leads to an energy splitting of singlet and triplet excited states. [A clear discussion of this is in Chapter 18, The Helium Atom, in Quantum Physics by Stephen Gasciorowicz.]