  In this paper, we shall study the stellar work of Norwegian mathematician
Selberg and Hungarian mathematician Erd\H{o}s in providing an Elementary proof
of the well-known \textit{Prime Number Theorem}. In addition to introducing
ourselves to the notion of \textit{Arithmetic Functions}, we shall primarily
focus our research on obtaining suitable estimates for the \textit{Chebyshev
Theta Function} $\vartheta(x)$. Furthermore, we'll try to infer about the
asymptotic properties of another function $\rho(x)$, which shall be needed
later on in establishing an equivalent statement of our main result. All the
mathematical terminologies pertinent to the proof have been discussed in the
earlier sections of the text.
