Short answers, pulled from the story.
Special relativity rests on two postulates stated by Albert Einstein in his 1905 paper. The first is the principle of relativity: the laws of physics are identical for all observers moving at a constant speed. The second is the principle of light speed invariance: light travels through vacuum at the same speed for all observers, regardless of the motion of the source or the observer.
Einstein published special relativity on the 26th of September 1905 in a paper titled "On the Electrodynamics of Moving Bodies." The theory became essentially complete in 1907 when Hermann Minkowski published his papers on spacetime.
The 1887 Michelson-Morley experiment was designed to detect Earth's motion through the proposed aether, a medium thought to carry light waves. It found no difference in the speed of light along different directions, confirming the constant speed of light and showing that the aether did not exist.
Time dilation is the effect by which a moving clock runs slower than a stationary one. The effect is negligible at everyday speeds but becomes large near the speed of light. It has been confirmed experimentally through the extended lifetimes of high-speed muons produced by cosmic rays in Earth's outer atmosphere.
The twin paradox, articulated by Paul Langevin in 1911, involves a traveler who makes a high-speed round trip and returns to find far more time has passed on Earth than in their own experience. The asymmetry arises because the traveler must turn around and change their state of motion, breaking the symmetry between the two observers. Both twins agree on exactly how much each has aged once the trip is complete.
Special relativity predicts that mass and energy are equivalent, as expressed in the mass-energy equivalence formula. Einstein presented this argument in his 1905 paper "Does the Inertia of a Body Depend upon its Energy Content?" using conservation of energy and momentum and the relativistic Doppler shift formula. The Newtonian mass of an object equals its energy divided by the speed of light squared.