We introduce the Yale-Potsdam Stellar Isochrones (YaPSI), a new grid of stellar evolution tracks and isochrones of solar-scaled composition. In an effort to improve the Yonsei-Yale database, special emphasis is placed on the construction of accurate low-mass models (Mstar < 0.6 Msun), and in particular of their mass-luminosity and mass-radius relations, both crucial in characterizing exoplanet-host stars and, in turn, their planetary systems. The YaPSI models cover the mass range 0.15 to 5.0 Msun, densely enough to permit detailed interpolation in mass, and the metallicity and helium abundance ranges [Fe/H] = -1.5 to +0.3, and Y = 0.25 to 0.37, specified independently of each other (i.e., no fixed Delta Y/Delta Z relation is assumed). The evolutionary tracks are calculated from the pre-main sequence up to the tip of the red giant branch. The isochrones, with ages between 1 Myr and 20 Gyr, provide UBVRI colors in the Johnson-Cousins system, and JHK colors in the homogeneized Bessell & Brett system, derived from two different semi-empirical Teff-color calibrations from the literature. We also provide utility codes, such as an isochrone interpolator in age, metallicity, and helium content, and an interface of the tracks with an open-source Monte Carlo Markov-Chain tool for the analysis of individual stars. Finally, we present comparisons of the YaPSI models with the best empirical mass- luminosity and mass-radius relations available to date, as well as isochrone fitting of well-studied ste
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