The theory of special and general relativity were brought by Einstein. It is based on the realisation that newtonian dynamics did not work in some special cases. For example, it could not predict the orbit of mercury when it depicted a very accurate orbit of the other planets in the solar system.
He inspired his theory on previous work by Minkoswki (the Minkowski diagram-fig1), and on thelorentz transformation for special relativity and on the work done by maxwell and penrose for the general relativity.
What really is import not only to distinguish the 2 theories but also to understand relativity at its core is the frame of reference concept. Each frame of reference (abstract concept) has its own coordinate system with origin, orientation and scale as properties. A frame of reference can be either intertial meaning that it is at rest or moving at a constant speed in a uniform movment or non-inertial meaning that it is accelerating.
Special relativity
Einstein introduced special relativity (which main purpose is to explain the laws of physics when 2 objects are moving at a constant speed: inertial frame of refrence according to each other's perpective) in 1905 is based on 2 principles.
The laws of physics are the sale for all objects moving in inertial frame of reference
The speed of light -c- is the same for all observers regardkless of their motion to the light source
Here are a couple depiction of what a Minkowski diagram looks like.
Time dilation
Length contraction
Length contraction is a phenomena that happends at large velocity (close to the speed of light) and that goes along side with time dilation. It led to many parodoxes like the barn problem where you have a stick that is longer than the length of the barn and you're trying to get it to fit inside and close the barn doors. Is this possible?
The twin paradox
The special relativity theory led to paradoxes (which are not real ones because they have a solution).
Picture this situation: twins living on earth. On decide to leave for the Andrometa galaxy and travels there at a significant percentage of the speed of light while the other stays on earth. Knowing the principle of time dilation. When the twin comes back will he be younger than his brother? If so how many years would have passed by for each twin?
The doppler effect
We might all know the doppler effect but not under this name: when an ambulance is moving closer and closer and then away from you, the frequency of the waves get higher and higher as it is moving closer to you and lower when it is moving away from you. This is resulting in higher-pitched tones followed by lower pitched tones.
Those simulations might give you a better visual understanding of the principle:
