This paper studies the Hochschild cohomology of finite-dimensional monomial algebras. If Λ = K/I with I an admissible monomial ideal, then we give sufficient conditions for the existence of an embedding of $K[x₁,...,x_r]/⟨x_a{x}_{b}fora\ne b⟩$ into the Hochschild cohomology ring HH*(Λ). We also introduce stacked algebras, a new class of monomial algebras which includes Koszul and D-Koszul monomial algebras. If Λ is a stacked algebra, we prove that $HH*\left(\Lambda \right)/\cong K[x₁,...,x_r]/⟨x_a{x}_{b}fora\ne b⟩$, where is the ideal in HH*(Λ) generated by the homogeneous nilpotent elements. In...