You need either enumerate
or enumitem
to support that syntax.
However, there are some problems.
Let's consider the code
\documentclass{svmono}
\usepackage{showframe}
%\usepackage{enumerate}
\begin{document}
\begin{enumerate}
\item First level
\begin{enumerate}
\item Second level
\begin{enumerate}
\item Third level
\begin{enumerate}
\item Fourth level
\end{enumerate}
\end{enumerate}
\end{enumerate}
\item Two
\end{enumerate}
\begin{itemize}
\item First level
\begin{itemize}
\item Second level
\begin{itemize}
\item Third level
\begin{itemize}
\item Fourth level
\end{itemize}
\end{itemize}
\end{itemize}
\item Two
\end{itemize}
\end{document}
Output without packages

Output after adding \usepackage{enumerate}

Output after adding \usepackage{enumitem}

Output after adding \usepackage{enumitem}
with fixes.
\documentclass{svmono}
\usepackage{showframe}
\usepackage{enumitem}
\setlist[enumerate]{align=left}
\setlist[itemize]{align=left}
\begin{document}
\begin{enumerate}
\item First level
\begin{enumerate}
\item Second level
\begin{enumerate}
\item Third level
\begin{enumerate}
\item Fourth level
\end{enumerate}
\end{enumerate}
\end{enumerate}
\item Two
\end{enumerate}
\begin{itemize}
\item First level
\begin{itemize}
\item Second level
\begin{itemize}
\item Third level
\begin{itemize}
\item Fourth level
\end{itemize}
\end{itemize}
\end{itemize}
\item Two
\end{itemize}
\end{document}

Not really the same, but not so distant.
Code for your application
\documentclass{svmono}
\usepackage{showframe}
\usepackage{enumitem}
\setlist[enumerate]{align=left}
\setlist[itemize]{align=left}
\begin{document}
\begin{enumerate}[label=\roman*.]
\item One
\item Two
\end{enumerate}
\end{document}

Comments
The \usepackage{showframe}
line has been added just to properly show the bounding box of the text block. Remove it for your document.
Using enumerate
would change the appearance of all lists with respect to the svmono
standard, so it is out of question. With enumitem
the output is not very different.
svmono
is not a standard class, so it could be doing anything; the compilable code that Bernard mentioned would include using a standard class that we all have (article
would be best). The standard classes don't usually change how enumerate works, so you'd need a package to do that for you. Looking at the way you've written things, can you try adding\usepackage{paralist}
after the first line?enumitem
might be a more flexible choice. If loaded as\usepackage[shortlabels]{enumitem}
this particular syntax is supported