You can use the enumitem package to produce:

Here's the code:
\documentclass{article}
\usepackage{enumitem}
\setlist[enumerate,1]{label=\arabic*}
\setlist[enumerate,2]{label=\theenumi.\arabic*}
\setlist[enumerate,3]{label=\theenumii.\arabic*}
\begin{document}
\begin{enumerate}
\item Top Levek
\begin{enumerate}
\item Second Level
\begin{enumerate}
\item Third Level
\end{enumerate}
\end{enumerate}
\end{enumerate}
\end{document}
The important bits are the lines
\usepackage{enumitem}
\setlist[enumerate,1]{label=\arabic*}
\setlist[enumerate,2]{label=\theenumi.\arabic*}
\setlist[enumerate,3]{label=\theenumii.\arabic*}
These specify what you want the labels to look like. I highly recommend reading the package manual if you need to tweak further. It's very to easy to read.
Edit TO get the indentation in the OP you can use:
\documentclass{article}
\usepackage{enumitem}
\setlist[enumerate]{
leftmargin=0pt, labelindent*=0pt, labelwidth=0pt,align=left
}
\setlist[enumerate,1]{label=\arabic*}
\setlist[enumerate,2]{label=\theenumi.\arabic*}
\setlist[enumerate,3]{label=\theenumii.\arabic*}
\begin{document}
\begin{enumerate}
\item Top Level
\begin{enumerate}
\item Second Level
\begin{enumerate}
\item Third Level
\end{enumerate}
\end{enumerate}
\end{enumerate}
\end{document}
to give:

EDIT II As Mico says in the comments, for the required indentation it is easier to use \setlist[enumerate]{ wide=0pt }.
(a),(b), etc., not1.1,1.2, etc. Please also advise whether or not second-level enumerated items should be left-indented with respect to first-level enumerated items. – Mico Oct 29 '18 at 09:56