You should know that every periodic function can be expressed as a Fourier series, $f(\vec{r})=\sum\limits_{\vec{G}}f_{\vec{G}}\exp\left(i\vec{G}\cdot\vec{r}\right)$.
You should be able to determine the primitive reciprocal lattice vectors of any Bravais lattice and construct the reciprocal lattice vectors $\vec{G}_{hkl} = h\vec{b}_1 + k\vec{b}_2 + l\vec{b}_3$.
You should know that the reciprocal lattice of an orthorhombic lattice $(a,b,c)$ is also an orthorhombic lattice $(2\pi/a,2\pi/b,2\pi/c)$ and that
the reciprocal lattice of fcc is bcc and the reciprocal lattice of bcc is fcc.
Given a periodic function in 1, 2, or 3 dimensions, you should be able to determine the coefficients $f_{\vec{G}}$ of the corresponding Fourier series.
Know that the relation between the real space primitive lattice vectors and the reciprocal space lattice vectors is $\vec{a}_i\cdot\vec{b}_j = 2\pi\delta_{ij}$.
You should be able to describe what a plane wave is and give the formula for a plane wave.
