参考文献：

1. TiKZ入门教程 - LaTeX工作室 (latexstudio.net)
2. Latex-TiKZ绘制数学平面几何图教程_latex绘制几何图形-CSDN博客
3. 【TikZ 简单学习(上)：基础绘制】Latex下的绘图宏包-CSDN博客
4. LaTeX—Tikz 宏包入门使用教程 - 知乎 (zhihu.com)
5. Latex 实时编译 & TikZ 绘图

基本语法

首先 \usepackage{tikz} 导入包，基本的指令是：

\begin{center}
	\begin{tikzpicture}
		\coordinate(a1) at (0,0); 		%将坐标 (0,0) 标记为 a1
		\coordinate(a2) at (5,0);
		\coordinate(a3) at (0,5);
		\coordinate(a4) at (1,-1);
		
		\coordinate(b1) at (1,1);
		\coordinate(b2) at (2,1);
		\coordinate(b3) at (2,2);
		\coordinate(b4) at (1,2);
		
		\coordinate(c1) at (1,3);
		\coordinate(c2) at (4,4);
		\coordinate(c3) at (3,-3);
		
		\node at (a1)[left]{$a_1$};		%在位置 a1 书写标识
		\node at (a2)[above]{$a_2$};
		\node at (a3)[right]{$a_3$};
		\node at (a4)[below]{$a_4$};
		
		\node at (b2)[shift={(0.6,-0.2)},rotate=45]{let $b=\hat\alpha_\kappa \cdot \frac{1}{\beta}$};	%偏移+旋转
		
		\fill (a1) circle (0.5mm); 		%在位置 a1 绘制圆圈
		\fill (a2) circle (0.5mm);
		\fill (a3) circle (0.5mm);
		\fill (a4) circle (0.5mm);
		
		\fill (c1) circle (1mm);
		\fill (c2) circle (1mm);
		\fill (c3) circle (1mm);
		
		\draw[line width=0.3mm,color=blue] (a2) -- (a3);	%绘制从 a1 到 a2 的线段
		\draw[dash dot,->] (a1) -- (a2);					%箭头
		\draw[loosely dash dot,<->] (a1) -- (a3);			%双箭头
		\draw[] (b1)--(b2)--(b3)--(b4)--cycle;				%闭合线段
		
		\draw (a2) circle (1cm);						%圆圈
		\draw (a2) ellipse (1cm and 2cm);				%椭圆
		\draw[color=red] (a1) rectangle (a4);			%矩形
		
		\draw (a3) .. controls (c1) and (c2) .. (a2);	%由 c1,c2 控制的贝塞尔曲线
		\draw (a1) parabola bend (c3) (a2);				%以 c3 为顶点的抛物线
		
		\draw[step=1,color=gray!40] (-2,0) grid (0,4);				%绘制网格
		\draw[latex-latex, red] (0,2) -- ++(-1,1) -- ++(-1,-1);		%更新的偏移
		\draw[dashed, blue] (0,1) -- +(-1,1) -- +(-2,0);			%不更新的偏移
		
		\draw[domain=0:4] plot (\x,{0.1*exp(\x)}) node[right]{$f(x)=\frac{1}{10}e^x$};	%绘制函数图像
	\end{tikzpicture}
\end{center}

绘制结果：

高级功能

树形图：

\begin{center}
	\tikzset{
		box/.style ={
			rectangle, 				%矩形节点
			rounded corners=5pt, 	%圆角
			minimum width=50pt, 	%最小宽度
			minimum height=20pt, 	%最小高度
			inner sep=5pt, 			%文字和边框的距离
			draw=blue 				%边框颜色
		}
	}
	
	\begin{tikzpicture}[sibling distance = 80pt]	%树形图
		\node[box] {root}
		child {node[box] {a1}}
		child {node {a2}
			child {node {b1}}
			child {node {b2}}}
		child {node[box] {a3}};			
	\end{tikzpicture}
\end{center}

绘制结果：

关系图：

\begin{center}
	\usetikzlibrary{graphs}	%关系图
	\begin{tikzpicture}
		\graph {
			"$x_1$" -> "$x_2$"[red] -> "$x_3\|x_4$";
			"$x_1$" ->[bend left] "$x_3\|x_4$";
		};
	\end{tikzpicture}
	
	\begin{tikzpicture}
		\coordinate(a1) at (0,0);
		\coordinate(a2) at (5,0);
		\coordinate(a3) at (2,3);
		
		\node at (a1)[left]{$a_1$};
		\node at (a2)[above]{$a_2$};
		\node at (a3)[right]{$a_3$};
		
		\fill (a1) circle (0.5mm);
		\fill (a2) circle (0.5mm);
		\fill (a3) circle (0.5mm);
		
		\graph {
			(a1) -> (a2) -> (a3);
			(a1) ->[thick,blue,bend left,dashed] (a3);
		};
	\end{tikzpicture}
\end{center}

绘制结果：