Inertia
Albert Einstein's theory of special relativity, as proposed in his 1905 paper entitled "On the Electrodynamics of Moving Bodies" was built on the understanding of inertia and inertial reference frames developed by Galileo and Newton. While this revolutionary theory did significantly change the meaning of many Newtonian concepts such as mass, energy, and distance, Einstein's concept of inertia remained unchanged from Newton's original meaning (in fact, the entire theory was based on Newton's definition of inertia). However, this resulted in a limitation inherent in special relativity: the principle of relativity could only apply to reference frames that were "inertial" in nature (meaning when no acceleration was present). In an attempt to address this limitation, Einstein proceeded to develop his general theory of relativity ("The Foundation of the General Theory of Relativity," 1916), which ultimately provided a unified theory for both "inertial" and "noninertial" (accelerated) reference frames. However, in order to accomplish this, in general relativity, Einstein found it necessary to redefine several fundamental concepts (such as gravity) in terms of a new concept of "curvature" of space-time, instead of the more traditional system of forces understood by Newton.
Spacetime
Minkowski had been concerned with the state of electrodynamics after Michelson's disruptive experiments at least since the summer of 1905, when Minkowski and David Hilbert led an advanced seminar attended by notable physicists of the time to study the papers of Lorentz, Poincaré et al. However, it is not at all clear when Minkowski began to formulate the geometric formulation of special relativity that was to bear his name, or to which extent he was influenced by Poincaré's four-dimensional interpretation of the Lorentz transformation. Nor is it clear if he ever fully appreciated Einstein's critical contribution to the understanding of the Lorentz transformations, thinking of Einstein's work as being an extension of Lorentz's work.
On November 5, 1907 (a little more than a year before his death), Minkowski introduced his geometric interpretation of spacetime in a lecture to the Göttingen Mathematical society with the title, "The Relativity Principle" ("Das Relativitätsprinzip"). On September 21, 1908, Minkowski presented his famous talk, "Space and Time" ("Raum und Zeit"), to the German Society of Scientists and Physicians. The opening words of "Space and Time" include Minkowski's famous statement that "Henceforth, space for itself, and time for itself shall completely reduce to a mere shadow, and only some sort of union of the two shall preserve independence." "Space and Time" included the first public presentation of spacetime diagrams (Fig. 1‑4), and included a remarkable demonstration that the concept of the "invariant interval" (discussed below), along with the empirical observation that the speed of light is finite, allows derivation of the entirety of special relativity.