DLP Relationship of primitive roots $\pmod{p}$ with $p$ and $g$

Question

I have been following J Hoffsteins (et al) An Intro to Mathematical Cryptography.

I am interested in the relationship between the existence, frequency, and any patterns of Primitive Roots in relation to values of elements $g \in G$ and prime $p$ for the Discrete Log Problem (DLP):

$$g^{x}\pmod{p}=h$$

Seeking references to books, websites, videos and other material that explains this in depth.

I am new to group theory so items not too advanced / difficult would be appreciated