This line from Lewis Carroll's Through the Looking-Glass [1871], I think, is very appropriate for an article about mirrors. Two of the most famous mirrors of the Ancient World have been attributed to Archimedes, the earlier project for the Alexandrian Pharos, designed by Sostratus of Cnidus and built by Ptolemy III of Egypt. But, as it was completed around the time Archimedes was born [c.280 BC], he couldn't have designed the mirror. Although the Pharos' appearance is known from written accounts, images, and surviving masonry, the form of the beacon and the mirror is less certain. Speculation has made the former a bonfire, torches, or burning oil. Some say the mirror was concave and bronze, though Robert Temple suggests silver-backed glass, known at that time, "which had maximum reflexivity".
This property enhanced the beacon's light by night, and, so ancient writers tell us, enabled Ptolemy to observe distant ships by day. Thus, the mirror could've been used as an instrument of peace and war.
The military aspect brings me to the Siege of Syracuse in 212 BC. Here the elderly Archimedes was said to have used a "Burning Mirror" on the Roman fleet attacking his home town. As with the Pharos mirror, the design of what Temple termed "the first 'Death Ray' in history", has been debated for centuries. The simplest theory is that soldiers on cliff tops used highly polished shield backs to direct sunlight onto the Roman fleet. Among those attempting to recreate the "Burning Mirror" was the Comte de Buffon in the 1740s. A 128 mirror experiment, he said, "set fire to a plank of tarred fir at 150 feet", while a 45 mirror one "melted a tin bottle" at 20 ft. Yet just two models survive - one a grid of 48 adjustable mirrors, the other a strange flower-like object, the "petals" being adjustable wedge-shaped mirrors.
[The image combines an ancient mosaic of the Pharos and a "Burning Mirror"]

In Mexico we encounter a Mayan and Aztec god called Tezcatlipoca - "Smoking Mirror" - aka Hurakan, "One Foot".
Legend has it that the leg eaten by the Earth Monster, was replaced by an obsidian mirror. His name alluded to the mirror's "secrets" only being revealed when the smoke cleared. Andrew Lang, in the 19th century, noted that, in "successful experiments", crystal balls go misty, then black, before "the pictures emerge". Being a sorcerer, Tezcatlipoca used his mirror to see events unfold, into people's hearts and minds, and into the future. [Vulcan's Mirror also showed the past.] A neat spin on this is the "Mirror of Souls" in Terry Pratchett's Eric, owned by Lord Astfgl, King of the Demons. It is described as having a

"cool black surface...surrounded by an ornate frame, from which curls of greasy smoke constantly unfolded and drifted".

Jet, obsidian and anthracite mirrors are often found in "high status" Pre-Columbian graves. Donald Mackenzie said, in his Myths of Pre-Columbian America, that the Peruvians employed such mirrors in "crystallomancy". As with the Mayan Temple of Gucomatze's stone, they believed the gods could "communicate" via them. Tezcatlipoca also possessed a gold mirror, "Viewer", again used for divination. Mackenzie tells us that the Chinese used metal mirrors, especially copper, for scrying.
One of the most famous crystallomancers was the French prophet and mystic Nostradamus. In 1560 he's said to have revealed to Queen Catherine de Medici the fate of her sons as Kings of France. The scene in the Chateau Chamont is atmospherically evoked by John Hogue in Nostradamus & The Millennium [1987]:

"At midnight the Queen entered the dark laboratory... . Nostradamus, with candle in hand, motioned her into a magic circle traced on the stone floor before a magic mirror. On the mirror's corners were written the four Hebrew names of God: Yahweh, Elohim, Mitatron and Adonai, in pigeon's blood. He took her hand and began singing a gentle incantation to the Angel Anael to activate the mirror's power. Clouds of dim light played in the dark leaden glass molding a vision of another room stretching beyond the laboratory wall."

The number of times each son encircled this virtual chamber denoted their reigns in years. Like Alice's mirror world, this room could be seen as a "parallel universe/dimension". Through the Looking-Glass influenced the art of Escher, whose multiple viewpoints/perspectives used the spatial ambiguity created by reflections. His images of dream-like "impossible worlds" depict "alternative realities" that exist simultaneously in several dimensions.
Yet crystallomancy can be practised with any surface holding a reflection, as Pratchett's Witches Abroad illustrates.
By "sending her own image" via actual mirrors, Lily de Tempscire was able to view events through such media as water, ice and windows. To make herself omnipresent she employed two mirrors:

"For if images can steal a bit of you, then images of images can amplify you, feeding you back on yourself, giving you power.... .
And your image extends forever, in reflections of reflections, and every image is the same, all the way around the curve of light."

If you've ever been in a store changing room or a theatre dressing room, you'll know what Pratchett means. Your multiple reflection appears to stretch out to infinity. It's a surreal and unsettling experience .