\documentclass{article}
\begin{document}
   hello, world
\end{document}

\documentclass{article}

\usepackage{Ctex}

\author{yif}

\title{我是标题}

\begin{document}

\maketitle

我是yif % This is comment

\end{document}

\documentclass{article}
\usepackage{Ctex} 
      \title{我是标题}
    \author{yif} 
\begin{document} 
  \maketitle 
  \section{Hello China} 
    China is in East Asia.
    \subsection{Hello Beijing} 
    Beijing is the capital of China.
      \subsubsection{Hello Dongcheng District} 
        \paragraph{Tian‘anmen Square}is in the center of Beijing %段落
          \subparagraph{Chairman Mao} is in the center of Tian‘anmen Square 
      \subsection{Hello Guangzhou} 
        \paragraph{Sun Yat-sen University} is the best university in Guangzhou. 
\end{document}

\documentclass{article} 
\usepackage{Ctex}
\begin{document} 
   \tableofcontents %生成目录
   \section{Hello China} China is in East Asia. 
     \subsection{Hello Beijing} Beijing is the capital of China. 
       \subsubsection{Hello Dongcheng District} 
         \paragraph{Hello Tian‘anmen Square}is in the center of Beijing 
           \subparagraph{Hello Chairman Mao} is in the center of Tian‘anmen Square 
\end{document}

\documentclass{article} 
\usepackage{Ctex}
\title{我的标题}
\author{yif}
    \begin{document} 
\maketitle 
   Beijing is 
   the capital 
   of China. 

  Washington is 

   the capital 

   of America. 

   Amsterdam is \\ the capital \\ 
   of the Netherlands. 
    \end{document}

\documentclass{article} 
       \usepackage{amsmath} 
       \usepackage{amssymb}
    \usepackage{Ctex}
    \title{我的标题}
    \author{yif} 
\begin{document} 
\maketitle
   The Newton‘s second law is F=ma. 

   The Newton‘s second law is $F=ma$. %用美元修饰数学公式

   The Newton‘s second law is 
  
F=ma


   The Newton‘s second law is 
  
F=ma


   Greek Letters $\eta$ and $\mu$ %用数学符号

   Fraction $\frac{a}{b}$ %表示分数

   Power $a^b$ %表示指数

   Subscript $a_b$ %b是a的下标

   Derivate $\frac{\partial y}{\partial t} $ %偏导数

   Vector $\vec{n}$ %向量

   Bold $\mathbf{n}$ %加粗

   To time differential $\dot{F}$ %用点表示微分

   Matrix (lcr here means left, center or right for each column)%矩阵 
   \[ 
     \left[ 
       \begin{array}{lcr} 
         a1 & b22 & c333 \\ 
         d444 & e555555 & f6 
       \end{array} 
     \right] 
   \] 

Equations(here \& is the symbol for aligning different rows) %写&
\begin{align} 
   a+b&=c\\ %公式后面显示标号
   d&=e+f+g %公式后面显示标号
\end{align} 

\[ %带前括号
   \left\{ 
     \begin{aligned} 
       &a+b=c\\ 
       &d=e+f+g 
     \end{aligned} 
   \right. 
\]

\end{document}