The discovery of systems, which at low temperatures have an electric resistance that vanishes, has attracted great attention due to the possibility of dissipationless energy transport. This phenomenon, called superconductivity, is presented here with a survey of some characteristic experimental properties and their initial theoretical explanation through the London theory. Microscopic considerations lead to the idea of Cooper pairs between electrons as giving origin to the phenomenon, with the proposed binding between the electrons as the result of an attractive interaction that originates in exchanges of phonons between the electrons. A full mean-field theory was presented successfully by Bardeen-Cooper-Schrieffer to explain the so-called conventional superconductors. Interesting phenomena, such as magnetic flux quantization, tunneling between macroscopic systems (Josephson effect), and the existence of magnetic flux vortices, are discussed, together with the existence of different types of superconductors, including nonconventional ones. The excitations are discussed leading to the existence of a gap in the spectrum or even gapless cases due to unconventional pairings or due to the presence of magnetic fields, and the modes are discussed in the context of the Goldstone and Anderson-Higgs mechanisms.