High-pressure methane sorption isotherms at 40-101 degrees C and pressures up to 25 MPa were measured on Jurassic lacustrine and Silurian marine shales from China. Shale samples span a thermal maturity range from low mature (oil window) to overmature (dry gas window). Low-pressure CO2 and N-2 adsorption techniques were used to quantify specific surface area, pore volume, and pore size distributions. The thermodynamic characteristic of methane sorption on shales was assessed based on the experimental multitemperature isotherms. The effects of physical and chemical properties of shales on thermodynamic properties were analyzed and discussed. Finally, standard enthalpy of sorption was first introduced to evaluate the sorption affinity of methane on shales, and a general pattern describing the evolution of methane sorption as a function of thermal maturity was proposed. The Langmuir sorption capacity of these shales varies from 0.09 to 0.16 mmol/g. The low total organic matter carbon, clay-rich lacustrine shales have comparable methane sorption capacities as those of organic-rich, high thermal maturity marine shales, though high thermal maturity shale samples tend to have larger micropore volume than low mature shales. Clay minerals, especially I/S mixed layer minerals, contribute a lot to methane sorption of lacustrine shales in oil window. The isosteric heat of methane sorption on these shales decreases with increasing absorbed amount. The commonly used Clausius-Clapeyron equation, which neglects the real gas behavior and adsorbed volume, tends to overvalue the isosteric heat. The standard enthalpy of sorption reflects the comprehensive effect of physical and chemical properties of shales on gas sorption and shows a parabolic-like pattern with thermal maturity. The standard enthalpy of sorption first decreases with increasing thermal maturity up to the condensate window shales (late mature, equilibrated vitrinite reflectance 1.0-1.1%) and subsequently increases toward the overmature shales.