  Poincar\'e and Eisenstein series are building blocks for every type of
modular forms. We define Poincar\'e series for Jacobi forms of lattice index
and state some of their basic properties. We compute the Fourier expansions of
Poincar\'e and Eisenstein series and give an explicit formula for the Fourier
coefficients of the trivial Eisenstein series. For even weight and fixed index,
finite linear combinations of Fourier coefficients of non-trivial Eisenstein
series are equal to finite linear combinations of Fourier coefficients of the
trivial one.
