In the twentieth century, althoughDIUM evidentItaly and remarkableIEMN works correctly studied Galileo’s[aut]Galileo InertiaInertia, giving fundamental insights, they did not grasp the nuances of Galileo’s[aut]Galileo concept, ideaIdeas and mechanism of Inertia in its intellectualIntellectual subtlety. Galileo offered crucial insights on the concept of inertia, and there are many studies on this subject. We think that much investigation remains before the processus of Galileo’s scientific thought is complete, and we can fully appreciate both his uncertainties and understandings in the field. We think that a full understanding of some aspects of Galileo’s concept of inertia is lacking. We try to fulfil this gap. This paper deals with Galileo’s[aut]Galileo conceptualisationConceptualisation of InertiaInertia as presented in the First Two Days of Dialogo sopra i due massimi sistemi del mondoDialogo sopra i due massimi sistemi del mondo tolemaico e copernicano (1632) and Last Two Days of DiscorsiDiscorsi e dimostrazioni matematiche intorno a due nuove scienze (1638). Our work consists in three main parts: scientific, historical, and historiographical. (1) After introducing Inertia scientifically, we present it into historical research from its embryonic statements respectively as ImpetusImpetus, lawsLaw and incorporated into PrinciplePrinciple of virtual lawsLaw. (2) We historically analyse Galileo’s[aut]Galileo inertialInertial paths, showing how, in specific physicalPhysical–geometrical circumstances, his ideasIdeas confront both circular and rectilinear InertiaRectilinear inertia. (3) We examine and discuss some of the most influential historiographical contributions in the range of Galileo’s Inertia––and––his mechanics. Our paper intends to offer an additional analysisAnalysis on the subject within the history of physicsHistory of Physics––and––intellectualIntellectual history of ideasIdeas, including both the relationship between physics–mathematics and the current historiographical debate.