Explicit Values for Ramanujan's Theta Function ϕ(q)

This paper provides a survey of particular values Ramanujan's theta function $\varphi(q)=\sum_{n=-\infty}^{\infty}q^{n^2}$, when $q=e^{-\pi\sqrt{n}}$, where $n$ is positive rational number. First, descriptions the tools used to evaluate functions are given. Second, classical briefly discussed. Third, certain due Ramanujan and later authors Fourth, methods that determine these described. Lastly, an incomplete evaluation found in lost notebook, but now completed proved, discussed with sketch its proof.