\documentclass{article}
\usepackage{mathtools}
\usepackage{amsmath}
\usepackage{amssymb}
\begin{document}

\[
  1+1
\]

\begin{align}
  2+2 = 4\\[1ex]
  3+3 = 6
\end{align}

\begin{equation}
  \left(
    f(x) = 3
  \right)
  \left.
    f(x) = 3
  \right.
\end{equation}

Test $[ ... )$ of unmatched brackets in
inline math text.

In R, there is the operator \verb|[<-|...
that ...

\begin{equation*} 
  \left \{ 
    \begin{aligned}
      -\Delta \theta &= u \quad \text{in } \Omega, \\
      \theta &=0 \quad \text{on } \Gamma.
    \end{aligned}
  \right.
\end{equation*}

\begin{equation} \label{eq:state2}
  \left\{
    \begin{aligned}
      -\div [a_M(z)\nabla y + b(\nabla y)]  &= u \quad \text{in } \Omega, \\
      y &=0 \quad \text{on } \Gamma.
    \end{aligned}
  \right.
\end{equation}

\begin{equation}
  \left\{
    \begin{aligned}
      \min_{u,y} &J(u,y) \\
      \text{s.t.} \quad
                 &
                 -\Delta y = u \text{in } \Omega\\
                 y = 0 \text{on } \partial\Omega.
                 \\
                 &\begin{aligned}[t]
                   -\Delta y &= u && \text{in } \Omega\\
                   y &= 0 && \text{on } \partial\Omega.
                 \end{aligned}
    \end{aligned}
  \right.
\end{equation}

\end{document}