"The stellar mass content of galaxies is a key parameter to determine their properties and assess their evolution (e.g. via evolution of the stellar mass function [SMF] and scaling relations). However, our ability to measure stellar masses is limited by large systematic uncertainties and biases, which can reach up to factors of several for the youngest and most actively star-forming galaxies. One of the main problems is that the optical and near infrared (NIR) light that traces the stellar mass does it in a very non-linear way: the oldest stars and the most dust enshrouded ones can dominate the stellar mass although globally dimmer than the young and unobscured ones. ""SteMaGE"" is a systematic multi-wavelength effort to devise a methodology to properly weigh the stellar mass of the different components, resolved in time (via optical spectroscopy to constrain the star formation history [SFH]) and space (via spatially resolved analysis). Two state-of-the-art surveys, KINGFISH, ~65 galaxies imaged in the far IR with Herschel, and CALIFA, with spatially resolved ""integral field"" spectroscopy for ~600 galaxies, will be complemented with optical and NIR imaging. At each position in a galaxy the stellar mass density will be computed by comparing the observed optical/NIR emission with a library of models that reproduce different SFHs and dust attenuation. The far IR and spectral information will refine the prior distribution of models and reduce systematic uncertainties. These ""optimal"" stellar mass densities will be integrated and used to calibrate ""cheaper"" estimators based on fewer global optical/NIR fluxes. These can be adopted on large surveys, yielding systematic uncertainties of 10-20%. This new standard will be used to estimate the local SMF, providing a new unbiased reference for galaxy evolution models. The stellar mass maps will be used to unveil the real structure of galaxies and assess the importance of internal dynamical processes in galaxy evolution."