|German zoologist-philosopher Ernst Haeckel's 1899 composition table defining what he then believed to be the composition of the universe: mass and ether. |
In science, ether or aether, ἀἰθήρ (Greek) (Ѻ), from the Greek αἴθω (aíthō) meaning “to burn or light” (Ѻ), is a hypothetical medium, thought to exist, prior to Einstein (1905), that was supposed to fill all space; originally conceptualized as that which carried the celestial bodies in rotation about the earth and later conceived as being the medium (luminiferous ether) that carried light waves. 
In c.460BC, Greek philosopher Anaxagoras said to have postulated the existence of the element “aether”, which he conceived of as being in constant rotation and carried with it the celestial bodies. 
In c.455BC, Empedocles, under the supposed influence of Anaxagoras, was employing the term “ἀἰθήρ” (Fragment DK38), which some translated as “ether” (Leonard, 1908), “air” (Burnet, 1920), or “aither” (Inwood, 1992) as a seeming unstated fifth element in his fragments, such as:
“Come then! I shall tell you first the source from which the sun in the beginning and all other things which we now see became clear: earth and billowy sea and fluid air and the Titan aither squeezing all the them around in a circle.”— Empedocles (c.455BC), Fragment I39 / DK38
“For when aither separated and flew off from air and fire, and evolved into a heaven revolving in a very wide orbit, then fire - which had remained a little apart from the heaven - itself also grew into the rays of the sun. Earth withdrew into one place and when solidified by necessity it emerged and settled in the middle. Moreover, aither, being much lighter, moves all around it without diversion.”— Empedocles (c.455BC), Fragment I40 / A49a; cited by Philo of Alexandria (c.20AD) in On Providence
Empedocles, of note, commonly is not typically attributed to be an ether theorist, but rather only a four element and two force theorist. There may be some sort of translation issue here? Clara Millerd, in her On the Interpretation of Empedocles (1908) dissertation (§:The Elements) (Ѻ), e.g., gives a rather decent discussion how Empedocles refers (Fragment I12 / DK6) to the four roots or elements as: Zeus, Hera, Aidoneus, and Nestis, but in a confusing way in respect to which god represents which element, and also how he used the term ἀἰθήρ to characterize the “bright sky”.
In 1637, Rene Descartes, in his Discourse on Method (section: What Do Heat and Light of Fire Consist In?), and his 1641 Meditations (primarily the Third), argues that cold is merely the absence of heat, that darkness is the absence or recess of ethereal substance of the heat of fire (or stars), discusses good and evil, and intertwines these in with discussion on the possible existence a deity. Descartes thought of light as a pressure in the ether and color an effect of the rotation of the ether particles.
In 1842, Scottish chemistry Thomas Graham published Elements of Chemistry, wherein he discussed the ‘material theory of heat’ (an adaption of the caloric theory), in which heat was considered as indestructible particles, and the ‘undulatory theory of heat’ (an adaption of the undulatory of light), in which undulations in imponderable medium of space or ether are propagated that produce the impression of heat.  This may have been a precursor to Scottish engineering physicist William Rankine’s 1849 theory of “molecular vortices”, and possibly, in turn, William Thomson's later theory of quasi-labile ether of light propagation.
In 1887, Albert Michelson and Edward Morley, at Case Western Reserve University, Cleveland, Oh, performed their now-famous “Michelson-Morley experiment” (Ѻ), in which they used mirrors mounted on a stone slab that floated in a annual trough of mercury, in an attempt to measure “luminous ether”; they did not detect the presumed to exist “ether”.
In 1889, Willard Gibbs published an article comparing the electromagnetic wave theory of light with William Thomson’s ether theory. 
In 1898, Russian psychologist Nicolas von Grot postulated the concept of “psychic energy” and reasoned that the conscious processes take place not in nervous matter, but in the ether of the mind, or something along these lines. 
In 1899, German zoologist-philosopher Ernst Haeckel intermixed his affinity theory of everything with ether theory logic. 
In 1905, Einstein disabused the notion of 'ether', the medium in which electromagnetic waves were thought to be propagating, from physics.
Not to be confused with “ether” defined in chemistry as an oxygen atom connected to two alkyl or aryl groups, of general formula R–O–R'
The following are related quotes:
“Light waves were, after all, nothing more than undulatory states of empty space, and [thus] space gave up its passive role as a mere stage for physical events. The ether was invented and was admitted as a new kind of matter. It was over looked that by this procedure space itself had been brought to life.”— Albert Einstein (1929), “Field Theories, Old and New” 
“If the Michelson–Morley experiment had not brought us into serious embarrassment, no one would have regarded the relativity theory as a (halfway) redemption.”— Albert Einstein (c.1940), Publication 
1. Bothamley, Jennifer. (2002). Dictionary of Theories: One Stop to more than 5,000 Theories (§:Aether (either), pg. 13). Visible Ink.
2. Haeckel, Ernst. (1899). The Riddle of the Universe: at the Close of the Nineteenth Century (translator: Joseph McCabe) (ether table, pg. 229). Harper & Brother, 1900.
3. Freely, John. (2012). Before Galileo: the Birth of Modern Science in Medieval Europe (aether, pg. 287). Penguin.
4. Graham, Thomas. (1858). Elements of Inorganic Chemistry, (section: “Nature of Heat”, pgs. 96-97). Blanchard and Lea.
5. Gibbs, J. Willard. (1889). “A comparison of the electrical theory of light with Sir William Thomson's theory of a quasi-labile ether”, American Journal of Science. 3rd series, 37:129–144.
6. (a) Von Grot, Nicolas. (1898). “Die Begriffe der Seele und der Psychischen Energie in der Psychologie” (“The Terms of the Soul and the Psychic Energy in the Psychology”), Archiv fur systematische Philosophie, IV.
(b) Anon. (1898). Mind, Vol. 7, (pg. 591). B. Blackwell.
7. (a) Einstein, Albert. (1929). “Field Theories, Old and New”, New York Times, Feb 3.
(b) Swenson, Loyd S. (1972). The Ethereal Aether (pg. 223). University of Texas Press, 2013.
8. Folsing, Albrecht. (1998). Albert Einstein: a Biography (pg. 219). Penguin Group.
● Burich, Keith R. (1996). “Henry Adams and the Rise and Fall of Luminiferous Ether” (pg. 63), Proceedings of the Massachusetts Historical Society, 107:57-84.
● Aether (classical element) – Wikipedia.
● Aether theories – Wikipedia.