The logical structure of classical thermodynamics is presented in a modern, geometrical manner. The first and second law receive clear, operatively oriented statements and the Gibbs free energy extremum principle is fully discussed. Applications relevant to chemistry, such as phase transitions, dilute solutions theory and, in particular, the law of mass action, are also addressed in a very detailed and novel manner. The material is best suited to graduate level students and professors, and it brings classical thermodynamics closer to other branches of university physics where geometry plays a key role.