This textbook aims to briefly outline the main directions in which the

geometrization of thermodynamics has been developed in the last decades.

The textbook is accessible to people trained in thermal sciences but not

necessarily with solid formation in mathematics. For this, in the first chapters

a summary of the main mathematical concepts is made. In some sense,

this makes the textbook self-consistent. The rest of the textbook consists of

a collection of results previously obtained in this young branch of thermodynamics.

The manner of presentation used throughout the textbook is

sciences.