This textbook aims to briefly outline the main directions in which thegeometrization of thermodynamics has been developed in the last decades. The textbook is accessible to people trained in thermal sciences but notnecessarily with solid formation in mathematics. For this, in the first chaptersa summary of the main mathematical concepts is made. In some sense,this makes the textbook self-consistent. The rest of the textbook consists ofa collection of results previously obtained in this young branch of thermodynamics. The manner of presentation used throughout the textbook isadapted for ease of access of readers with education in natural and technicalsciences.