`Chiral Condensate with maximally twisted mass fermions' Abstract: We study the ‘spectral projector’ method for the computation of the chiral condensate and the topological susceptibility, using N_f=2 and N f = 2 + 1 + 1 dynamical flavors of maximally twisted mass Wilson fermions. In particular, we perform a study of the quark mass dependence of the chiral condensate Σ in the range 270 MeV < m_pi < 500 MeV and the continuum limit and compare our data with other calculations. In addition, we compute χtop in the quenched approximation where we match the lattice spacing to the Nf =2+1+1 dynamical simulations. Using the Kaon, η and η′ meson masses computed on the Nf = 2 + 1 + 1 ensembles, we then perform a preliminary test of the Witten-Veneziano relation.