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