The Monχey project will provide a large and homogeneous set of stellar yields for the low- and intermediate- mass stars and has applications particularly to galactic chemical evolution modelling. We describe our detailed grid of stellar evolutionary models and corresponding nucleosynthetic yields for stars of initial mass 0.8 M⊙ up to the limit for core collapse supernova (CC-SN) ≈ 10 M⊙. Our study covers a broad range of metallicities, ranging from the first, primordial stars (Z = 0) to those of super-solar metallicity (Z = 0.04). The models are evolved from the zero-age main-sequence until the end of the asymptotic giant branch (AGB) and the nucleosynthesis calculations include all elements from H to Bi. A major innovation of our work is the first complete grid of heavy element nucleosynthetic predictions for primordial AGB stars as well as the inclusion of extra-mixing processes (in this case thermohaline) during the red giant branch. We provide a broad overview of our results with implications for galactic chemical evolution as well as highlight interesting results such as heavy element production in dredge-out events of super-AGB stars. We briefly introduce our forthcoming web-based database which provides the evolutionary tracks, structural properties, internal/surface nucleosynthetic compositions and stellar yields. Our web interface includes user- driven plotting capabilities with output available in a range of formats. Our nucleosynthetic results will be available for further use in post processing calculations for dust production yields.