Einstein and Relativity
Table of Contents:
Introduction

Classical Observations of Mercury

The Planet Vulcan

Applying Relativity to Mercury's Orbit

Further Applications of Relativity

Bibliography
Albert Einstein published a number of essays between 1905 and 1915 and won the Nobel Prize for the one on the Photoelectric Effect in 1921. 
The essay on his theory of Special Relativity was published in 1905 and proposed that the laws of physics are the same in all inertial (not accelerating) reference frames and that the speed of light in a vacuum is the same for all observers, a constant.  This runs counter to the laws of physics as understood by Newton and Galileo where lengths in space and time are constant and speed depends on the speed of the reference frame.
Ten years later in 1915 Einstein published his theory of General Relativity, which included acceleration, counted gravity as a kind of acceleration, and deduced that gravity can "bend" or "warp" space itself.

Einstein's theory of Special Relativity was used to explain the failure of the 1887 Michelson-Morley experiment to find changes in the speed of light. 

Evidence for the General theory of Relativity was found when the bending of light due to warped space is observed by a British expedition during a total solar eclipse in 1919.  It was also used to predict the orbit of Mercury to a greater accuracy than ever before.
Einstein ca. 1920
Image source:https://www.mpp.mpg.de/english/institute/instGeschichte/einstein-en/index.html