1. Split equations with alignment
   1. \begin{equation}\begin{split}
   2. H_c&=\frac{1}{2n} \sum^n_{l=0}(-1)^{l}(n-{l})^{p-2}
   3. \sum_{l _1+\dots+ l _p=l}\prod^p_{i=1} \binom{n_i}{l _i}\\
   4. &\quad\cdot[(n-l )-(n_i-l _i)]^{n_i-l _i}\cdot
   5. \Bigl[(n-l )^2-\sum^p_{j=1}(n_i-l _i)^2\Bigr].
   6. \end{split}\end{equation}
2. Split
   1. \begin{split}
   2. a& =b+c-d\\
   3. & \quad +e-f\\
   4. & =g+h\\
   5. & =i
   6. \end{split}
3. Equation
   1. \begin{equation}
   2. a=b
   3. \end{equation}
4. Multline
   1. \begin{multline}
   2. a+b+c+d+e+f\\
   3. +i+j+k+l+m+n
   4. \end{multline}
5. Others
   1. \sqrt[\leftroot{-2}\uproot{2}\beta]{k}
   2. Roots
   3. A\xleftarrow{n+\mu-1}B\xrightarrow[T]{n\pm i-1}C
   4. Extensible arrows
   5. \boxed{\eta \leq C(\delta(\eta) +\Lambda_M(0,\delta))}
   6. Boxed formulas
   7. \begin{equation}
   8. \frac{1}{k}\log_2 c(f)\;\tfrac{1}{k}\log_2 c(f)\;
   9. \sqrt{\frac{1}{k}\log_2 c(f)}\;\sqrt{\dfrac{1}{k}\log_2 c(f)}
   10. \end{equation}
   11. Fraction
   12. 2^k-\binom{k}{1}2^{k-1}+\binom{k}{2}2^{k-2}
   13. binomial expressions
   14. Multiline subscripts and superscripts
   15. \sum_{\substack{
   16. 0\le i\le m\\
   17. 0<j<n}}
   18. P(i,j)
   19. \sum_{\begin{subarray}{l}
   20. i\in\Lambda\\ 0<j<n
   21. \end{subarray}}
   22. P(i,j)
   23. \begin{CD}
   24. S^{\mathcal{W}_\Lambda}\otimes T @>j>> T\\
   25. @VVV @VV{\End P}V\\
   26. (S\otimes T)/I @= (Z\otimes T)/J
   27. \end{CD}
6. Gather
   1. \begin{gather}
   2. a_1=b_1+c_1\\
   3. a_2=b_2+c_2-d_2+e_2
   4. \end{gather}
7. Align
   1. \begin{align}
   2. a_1& =b_1+c_1\\
   3. a_2& =b_2+c_2-d_2+e_2
   4. \end{align}
   5. \begin{align}
   6. a_{11}& =b_{11}&
   7. a_{12}& =b_{12}\\
   8. a_{21}& =b_{21}&
   9. a_{22}& =b_{22}+c_{22}
   10. \end{align}
   11. \begin{align}
   12. x& = y_1-y_2+y_3-y_5+y_8-\dots && \text{by wq}\\
   13. & = y’\circ y^* && \text{by Bruce}\\
   14. & = y(0) y’ && \text {by Axiom}
   15. \end{align}
   16. \begin{align}
   17. x&=y & X&=Y & a&=b+c\\
   18. x’&=y’ & X’&=Y’ & a’&=b\\
   19. x+x’&=y+y’ & X+X’&=Y+Y’ & a’b&=c’b
   20. \end{align}
   21. Equation groups with mutual alignment
8. Alignment building blocks
   1. \begin{equation*}
   2. \left.\begin{aligned}
   3. B’&=-\partial\times E,\\
   4. E’&=\partial\times B - 4\pi j,
   5. \end{aligned}
   6. \right\}
   7. \qquad \text{Maxwell’s equations}
   8. \end{equation*}
   9. P_{r-j}=
   10. \begin{cases}
   11. 0& \text{if $r-j$ is odd},\\
   12. r!\,(-1)^{(r-j)/2}& \text{if $r-j$ is even}.
   13. \end{cases}
9. Matrices
   1. \bigl( \begin{smallmatrix}
   2. a&b\\ c&d
   3. \end{smallmatrix} \bigr)
   4. smallmatrix
   5. \begin{pmatrix}
   6. D_1t&-a_{12}t_2&\dots&-a_{1n}t_n\\
   7. -a_{21}t_1&D_2t&\dots&-a_{2n}t_n\\
   8. -a_{n1}t_1&-a_{n2}t_2&\dots&D_nt
   9. \end{pmatrix}
   10. pmatrix