Short answers, pulled from the story.
Magnetism is the class of physical attributes that occur through a magnetic field, allowing objects to attract or repel each other. It is one of two aspects of electromagnetism, arising from electric currents and the magnetic moments of elementary particles.
The types of magnetism include diamagnetism, paramagnetism, ferromagnetism, antiferromagnetism, ferrimagnetism, and superparamagnetism, along with newer forms such as Nagaoka magnetism. Diamagnetism appears in all materials, while ferromagnetism, found in iron, nickel, and cobalt, produces the effects most people notice in everyday life.
Ferromagnetism occurs in only a few substances, the most common being iron, nickel, cobalt, their alloys, and some alloys of rare-earth metals. Every ferromagnetic substance has a Curie temperature above which it loses its ferromagnetic properties.
Hans Christian Orsted, a professor at the University of Copenhagen, discovered in 1819 that an electric current could create a magnetic field after noticing a compass needle twitch near a wire. The episode is known as Orsted's Experiment, and electromagnetism was discovered in 1820.
All known magnets are dipoles, and cutting a bar magnet in half produces two smaller bar magnets, each with its own north and south pole. An isolated pole, called a magnetic monopole, has never been observed despite systematic searches since 1931.
At high temperatures, random thermal motion makes it harder for electrons to maintain their alignment, weakening magnetism. Heating a ferromagnet to its Curie point disorders its magnetic domains and removes its magnetic properties, which return spontaneously when the material is cooled.
Diamagnetism, paramagnetism, and ferromagnetism can be fully explained only with quantum theory, since the Bohr-Van Leeuwen theorem shows diamagnetism is impossible under classical physics. Walter Heitler and Fritz London built a successful quantum model in 1927, introducing the exchange interaction central to the origin of magnetism.