\documentclass[10pt,a4paper]{article}
\usepackage[utf8]{inputenc}
\usepackage{geometry}
\usepackage[svgnames]{xcolor}
\geometry{footskip=15pt}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{tocloft}
\makeatletter
\let\stdl@section\l@section
\renewcommand*{\l@section}[2]{%
\stdl@section{\textcolor{blue}{#1}}{\textcolor{blue}{#2}}}
\let\stdl@subsection\l@subsection
\renewcommand*{\l@subsection}[2]{%
\stdl@subsection{\textcolor{DarkGreen}{#1}}{\textcolor{DarkGreen}{#2}}}
\AtBeginDocument{%
\let\nl@org@contentsline\contentsline
\def\contentsline#1{%
\def\nl@current@levelname{#1}%
\nl@org@contentsline{#1}%
}%
}
% \numberline evaluates \nl@current@levelname to find
% the horizontal alignment
\protected\def\numberline#1{%
\begingroup
\edef\nl@align{%
nl@align@%
\@ifundefined{nl@current@levelname}{}{\nl@current@levelname}%
}%
\edef\nl@align{%
\@ifundefined{\nl@align}\nl@align@{\csname\nl@align\endcsname}%
}%
\@ifundefined{nl@numberline@\nl@align}{%
\errmessage{Unknown alignment '\nl@align' for \noexpand\numberline}%
\nl@numberline@l{#1}%
}{%
\csname nl@numberline@\nl@align\endcsname{#1}%
}%
\endgroup
}
% Implementations of `\numberline` for the different horizontal alignments
\newcommand*{\nl@numberline@l}[1]{% left-aligned
\hb@xt@\@tempdima{#1 \hfil}%
}
\newcommand*{\nl@numberline@c}[1]{% centered
\hb@xt@\@tempdima{\hfil#1 \hfil}%
}
\newcommand*{\nl@numberline@r}[1]{% right-aligned
\hb@xt@\@tempdima{\hfil#1 }%
}
% Configuration
% -------------
% Horizonal alignment in \numberline:
% l: left-aligned
% c: centered
% r: right-aligned
% \nl@align@: Default setting
% \nl@align@<levelname>: Setting for specific level
\def\nl@align@{r}% default
\def\nl@align@section{r}
\makeatother
\begin{document}
\tableofcontents
\newpage
\section{The First Section}
\section{The Exterior Algebra of Multiconvectors}
\subsection{Dual Space}
\subsection{Permuations}
\subsection{Multilinear Functions}
\subsection{The Symmetrizing and Alternating Operations}
\subsection{The Tensor Product}
\subsection{The Wedge Product}
\subsection{Associativity of The Wedge Product}
\subsection{A Basics for \textit{k}-Convector}
\section{Tangent Vectors in $\mathbb{R}^{n}$}
\subsection{Germs of Functions}
\subsection{The Tangent Space}
\subsection{Vector Fields}
\section{Differential Forms on $\mathbb{R}^{n}$}
\subsection{Differential 1-Forms and the Differential of a function}
\subsection{Differential \textit{k}-Forms}
\subsection{The Exterior Derivative}
\section{Manifolds}
\subsection{Differentiability of Mapping and Jacobians}
\subsection{Topological Manifolds, Compatible charts and Smooth Manifolds}
\subsection{Smooth Functions on a Manifold}
\subsection{Smooth Maps Between Manifolds}
\subsection{Diffeomorphisms}
\subsection{Partial Derivatives}
\section{Tangent Vectors and the Tangent Space}
\subsection{Bases For the Tangents Space at a Point}
\subsection{The Differential of a Map}
\section{The Tangent Bundle}
\subsection{The Topology of The Tangent Bundle}
\subsection{The Manifold Structure on The Tangent Bundle}
\section{Smooth Bump Functions}
\section{Vector Fields}
\subsection{Smoothness of a Vector Field}
\section{Differential 1-Forms}
\subsection{The Differential of a Function and Local Expression for a Diffecrential 1-Form}
\subsection{The Cotangent Bundle}
\end{document}



Spacing between section number and title can be made by using ~~ in \subsection{~~The title name} here is new spacing after right allingment in section number
\documentclass[8pt,a4paper]{article}
\usepackage[utf8]{inputenc}
\usepackage{geometry}
\usepackage[svgnames]{xcolor}
\geometry{footskip=15pt}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{tocloft}
\makeatletter
\let\stdl@section\l@section
\renewcommand*{\l@section}[2]{%
\stdl@section{\textcolor{blue}{#1}}{\textcolor{blue}{#2}}}
\let\stdl@subsection\l@subsection
\renewcommand*{\l@subsection}[2]{%
\stdl@subsection{\textcolor{DarkGreen}{#1}}{\textcolor{DarkGreen}{#2}}}
\AtBeginDocument{%
\let\nl@org@contentsline\contentsline
\def\contentsline#1{%
\def\nl@current@levelname{#1}%
\nl@org@contentsline{#1}%
}%
}
% \numberline evaluates \nl@current@levelname to find
% the horizontal alignment
\protected\def\numberline#1{%
\begingroup
\edef\nl@align{%
nl@align@%
\@ifundefined{nl@current@levelname}{}{\nl@current@levelname}%
}%
\edef\nl@align{%
\@ifundefined{\nl@align}\nl@align@{\csname\nl@align\endcsname}%
}%
\@ifundefined{nl@numberline@\nl@align}{%
\errmessage{Unknown alignment '\nl@align' for \noexpand\numberline}%
\nl@numberline@l{#1}%
}{%
\csname nl@numberline@\nl@align\endcsname{#1}%
}%
\endgroup
}
% Implementations of `\numberline` for the different horizontal alignments
\newcommand*{\nl@numberline@l}[1]{% left-aligned
\hb@xt@\@tempdima{#1 \hfil}% Distance between titles and page number
}
\newcommand*{\nl@numberline@c}[1]{% centered
\hb@xt@\@tempdima{\hfil#1 \hfil}%
}
\newcommand*{\nl@numberline@r}[1]{% right-aligned
\hb@xt@\@tempdima{\hfil#1 }%
}
% Configuration
% -------------
% Horizonal alignment in \numberline:
% l: left-aligned
% c: centered
% r: right-aligned
% \nl@align@: Default setting
% \nl@align@<levelname>: Setting for specific level
\def\nl@align@{r}% default
\def\nl@align@section{r}
\makeatother
\begin{document}
\tableofcontents
\newpage
\section{The First Section}
\section{The Exterior Algebra of Multiconvectors}
\subsection{~~Dual Space}
\subsection{~~Permuations}
\subsection{~~Multilinear Functions}
\subsection{~~The Symmetrizing and Alternating Operations}
\subsection{~~The Tensor Product}
\subsection{~~The Wedge Product}
\subsection{~~Associativity of The Wedge Product}
\subsection{~~A Basics for \textit{k}-Convector}
\section{Tangent Vectors in $\mathbb{R}^{n}$}
\subsection{~~Germs of Functions}
\subsection{~~The Tangent Space}
\subsection{~~Vector Fields}
\section{Differential Forms on $\mathbb{R}^{n}$}
\subsection{~~Differential 1-Forms and the Differential of a function}
\subsection{~~Differential \textit{k}-Forms}
\subsection{~~The Exterior Derivative}
\section{Manifolds}
\subsection{~~Differentiability of Mapping and Jacobians}
\subsection{~~Topological Manifolds, Compatible charts and Smooth Manifolds}
\subsection{~~Smooth Functions on a Manifold}
\subsection{~~Smooth Maps Between Manifolds}
\subsection{~~Diffeomorphisms}
\subsection{~~Partial Derivatives}
\section{Tangent Vectors and the Tangent Space}
\subsection{~~Bases For the Tangents Space at a Point}
\subsection{~~The Differential of a Map}
\section{The Tangent Bundle}
\subsection{~~The Topology of The Tangent Bundle}
\subsection{~~The Manifold Structure on The Tangent Bundle}
\section{Smooth Bump Functions}
\section{Vector Fields}
\subsection{~~Smoothness of a Vector Field}
\section{Differential 1-Forms}
\subsection{~~The Differential of a Function and Local Expression for a Diffecrential 1-Form}
\subsection{~~The Cotangent Bundle}
\end{document}

10.xetc. numbers, because in this case the alignment of the text in the ToC would be broken. But you can change the reserved width for the number of all ToC entries of the sub-section level and other levels without any problem. – Schweinebacke May 29 '17 at 05:56