Humankind's Greatest Steps refers to all those exciting developments and progress on the knowledge and understanding of the Moon in all its essence and nature, which were achieved during different historical periods and that allowed the ride there. My main purpose in this text is for the reader to discover and assimilate them. Similarly, the work aims to answer the basic question: How was it possible?To achieve these objectives, I begin by explaining the way in which prehistoric societies, with their characteristic mythological mentality, treated and understood our Moon as a goddess. Next, I argue about the origins of philosophy as a form of thought proper to ancient Greek society first, and Greco-Roman afterwards, and I describe the way in which our satellite was studied and understood in rational, philosophical terms. Something very different from what happens in societies of the medieval period, who studied astronomy with a markedly theological and supernaturalist mentality. Then I go on to the drastic turn that takes place with the arrival of the European Renaissance and the return to the rational form of thought; of this period the most notable astronomer is Nicolaus Copernicus, for having presented his heliocentric theory and for having placed the Moon in its correct place in the universe: a satellite of the Earth, our most faithful and closest celestial companion. Next, for the seventeenth century I expose the origins of modern science; and I show how the astronomers Johannes Kepler and Galileo Galilei, and the brilliant physicist Isaac Newton, made their invaluable contributions to understand and describe the lunar globe in scientific terms. Finally, I explain the consolidation of the Lunar Astronomy from the period of the Enlightenment, which occurred between the eighteenth and nineteenth centuries, with the participation of a select group of astronomers, mathematicians and physicists: the position and movement of the satellite are already known with enough precision to seriously propose a trip to it.Then, I explain how all that knowledge about the Moon acquired in the course of history is combined with the monumental scientific -technological developments of the 20th century: the engines based on liquid fuels, the powerful rockets propelled with them, the sophisticated spacecraft and the prodigious computers that guide them; all this to put the Man firmly on his way to the Moon. The Space Race, initiated in 1957, has its peak moment on July 20, 1969, when the first man-made spacecraft settles on the satellite surface, and about seven hours later the astronaut Neil Armstrong, when descending from the ship, pronounces that famous phrase: "This is a small step for a man, but a great leap for Mankind."At the end of the reading of the text, I trust that the reader will begin to feel the Moon a little closer and much more familiar.