# How is the a Fermi surface different from a Fermi sphere?

How is a Fermi surface (a surface in reciprocal space separating the occupied electron states from unoccupied states at $$T=0$$) different from a Fermi sphere? Is Fermi sphere a special case of Fermi surface?

Yes, a Fermi sphere is just a special case (and almost always an idealization). The shape of a real'' Fermi surface is discussed in Mermin and Ashcroft, but a quick search on google image gives examples of what they really look like in solids.
When the system is perfectly periodic, the Fermi surface is the level set associated to the Fermi energy $$E_{\mathrm{F}}$$, i. e. consisting of those Bloch momenta $$k$$ for which $$E_n(k) = E_{\mathrm{F}}$$ holds for some band index $$n$$. Note that this definition also works for insulators where the Fermi energy lies in a spectral gap. But then the Fermi energy is the empty set.
For homogeneous systems where the Hamiltonian is just the free Hamiltonian $$H = \frac{1}{2m} \bigl (- \mathrm{i} \hbar \nabla \bigr )^2$$, then the only energy band is $$E(k) = \frac{\hbar^2}{2m} k^2$$ so that the Fermi surface is a perfect sphere.