Short answers, pulled from the story.
Sir George Cayley (1773-1857) is widely acknowledged as the founder of modern aeronautics. He was first called the "father of the aeroplane" in 1846 and published the first scientific analysis of the forces of flight, identifying thrust, lift, drag, and weight as the four vector forces acting on an aircraft.
Aeronautics is the broader science covering the study, design, manufacturing, and operation of all air flight-capable machines, including lighter-than-air craft such as airships and balloons, and ballistic vehicles. Aviation is a subset of aeronautics referring to the art or practice of flight, and while it historically meant only heavier-than-air flight, it now includes balloons and airships as well.
Otto Lilienthal was the first person to make well-documented, repeated, successful flights with gliders, with his Berlin flight attempts in 1891 regarded as the beginning of human flight. His "Lilienthal Normalsegelapparat" is considered the first aeroplane produced in series, and the Maschinenfabrik Otto Lilienthal in Berlin is recognized as the first aeroplane production company in the world.
The Montgolfier brothers gave their first public demonstration to the French Academie des Sciences in 1783. Their balloons were made of paper and filled with hot smoky air, which they called "electric smoke."
La Caroline, a hydrogen balloon built by Jacques Charles and the Robert brothers, completed the first flight of over 100 km on the 19th of September 1784, traveling between Paris and Beuvry. The balloon followed Jean Baptiste Meusnier's proposals for an elongated dirigible design and featured an inner ballonet within an outer envelope.
Aerodynamics is divided into incompressible flow at subsonic speeds below Mach 1, compressible flow above Mach 1 where shock waves appear, and transonic flow in the intermediate range around Mach 1 where airflow over an object can be locally subsonic at one point and locally supersonic at another.