Which religion was the first monotheistic one? Was it Judaism or a religion which disappeared from practice?
Judaism is very old, but it was not originally monotheistic (see below).
An earlier instance of monotheistic or monotheistic-esque worship occurred in the form of Atenism, the worship of the deified sun-disk Aten in Ancient Egypt. The Pharaoh Amenhotep IV (later Akhenaten), reigning around 1353/1351-1336/1334 B.C., promoted it as an arguably monotheistic state religion for Egypt.
Worship of Aten predates Akhenaten, but under his rule Atenism morphed from a more traditional henotheism into something that could be recognised as monotheism. He first elevated Aten into the supreme god, and later declared Aten to be the only god. He seemed to have also banned the worship of other gods and idols. However, soon after Akhenaten's death, the previous cult of Ra was restored and Atenism came to an end.
Atenism under Akhenaten is usually cited as the first true monotheism, but it might have been inspired by earlier Egyptian thoughts. The Lord Carnarvon (1866-1923) has written:
In any case, Atenism's rise and demise predates the emergence of Judaism as a monotheistic religion by several hundred years.
Well, I did not think this was controversial; given @TylerDurden's reaction, apparently I'm mistaken, so here's some more elaboration:
The Jewish faith did not fully commit to monotheism until around the time of the Babylonian Captivity. Prior to that, the Jewish people were largely henotheistic, if not polytheistic. This is not at all a new concept.
That the switch to monotheism occurred around the same time the Jews were deported to Babylon is a mainstream view.
Even those who might not agree, recognises this is the consensus view.
Of course, one could get around all this by defining Judaism as only beginning when the Jews conclusively rejected the existence of any other god. Though that would be more of a semantics quibble really. As is arguing about "single-ruler cults" vs "relegions (sic)".
Although we usually recognise Judaism as the first monotheistic faith, the title may actually go to Zoroastrianism. Zoroastrianism was established around the 6th century BCE. In a nutshell, it abandoned the previous Persian pantheon and simplified it to
Although Judaism may be older than the 6th century BCE, Judaism was not a strictly monotheistic faith until the return of the Israelites from the Babylonian exile, which happens to be around the 6th century, from Persia.
Zoroastrianism survived as the state religion of Persia for a few centuries until Alexander the Great's arrival, after which it gradually declined. Most of the remaining Zoroastrians converted to Islam when it arrived (likely simplified by the monotheistic similarities), although there's still a lively community of Zoroastrians, many in Iran (150'000 - 2 million depending on who you ask).
In an appendix to his book "When Our World Became Christian", Paul Veyne studies the extent to which the concept of monotheism applies to Judaism. His main point is that the concept of monotheism ("there is only one God") can be differentiated from monolatrism ("ye shall worship only one God") only if the idea of "a non-existent deity" can be conceptualized. That idea appeared at one time; before that invention, people did not think of gods in terms of true/fake, but rather in terms of yours/others, or stronger/weaker. Paul Veyne references the relevant Scripture texts in which the transition from monolatrism to monotheism can be seen.
Apparently, the Babylonian captivity was a turning point because it exposed the Hebrew intellectual elites to concepts which were developed in more Eastern areas, notably Zoroastrianism. Though Zoroastrianism gained the status of "state religion" in Persia only later on, the basic concepts were older (the exact date is highly disputed, but the current consensus points to "some time in the 2nd millenium BC"). The ideas had begun to percolate to neighbouring Babylonia at the time the Hebrew were there. Among these concepts was the notion that there was a Supreme Deity (Ahura Mazda), and other "gods" were really subordinates, even proxies; every prayer sent to any god was ultimately brought to the attention of Ahura Mazda. In that sense, the other gods in Zoroastrianism were already at that time beginning to be perceived as proto-angels and demons, to be respected and/or feared, but not "gods" in the same sense of Ahura Mazda.
When the Hebrew came back from Babylon, monotheism crystallized in their minds: they now understood that a god could be fake, non-existent. This contrasts with what philosophers were thinking in 5th century BC Greece: for them, the "divinity" was basically the Cosmos, the order. Conceptual gods were a-plenty, e.g. Eros (for love) or Chronos (for time). They had no notion that a concept could be non-existent: if you can think about it, then it exists, and is part of the Cosmos, thus you can worship it.
Since monotheism was a gradual innovation, there are "intermediate states" and one cannot really pinpoint an exact year in which it happened. The term henotheism has been coined to describe these intermediaries. In the case of Europe and Middle-East, it seems that true monotheism emerged with Judaism in the 6th or 5th century BC, although some definitions of monotheism can include earlier Zoroastrianism or Atenism (as described by @Semaphore). (However, it can be said that when Akhenaten mandated what was effectively monolatry, he was more concerned about the mundane power of the Amun priesthood than the alleged fakeness of the other gods.)
In Egypt, Pharaoh Amenhotep IV started a new monotheistic religion and renamed himself Akenaten, moving to a new capital city Armana unsullied by the normal religion. This would be about 1350 BC to 1320 BC.
When he died, his son Tutankhamun reconciled with the old regime, and the city was abandoned. This heresy and the need to wipe out its existence is one reason why King Tut's tomb was left intact so that it could be found in the 1920s.
I know Sigmund Freud wrote a book "Moses and Monotheism" trying to tie Judaism's development to Akenaten, but most seem to be unconvinced.
Long before Judaism the god Ahura Mazda was worshipped in Persia. They had a number of Commandments which where very simular to the Ten Commandments, it is very likely Abraham based his religion on this older one or at least borrowed some elements
A pity question. Atenism was a sect that departed from the traditional polytheistic Egyptians but did not really catch on after the death of Amenhotep. One, as mentioned above, can make a case for its brief appearance being the first recorded monotheistic belief system. Also often overlooked is that Judaism as practiced during the first temple period was henotheistic, i.e., recognizing the existence of other deities while worshipping YHWH or El as the primary regional or ethnic deity. Judaism changed and became more monotheistic after the Mesopotamian diaspora due to the influence of Zoroastrianism under the Persians.
Let me give an input regarding Hinduism which is considered as a major polytheistic religion and one of the oldest in the history.
Hinduism is actually have another name, 'Sanathana Dharma', which is considered as the culture of India. Even though Hinduism now considered as a religion with all essence of this culture.
There are more than 33 Million Gods of Hinduism. Why Hindus worship so many gods and goddesses is a real mystery for most people. What is the role of Hinduism in a monotheistic religion question in here? It do have an important role because the ultimate message from Hinduism lead to the concept of single God or all Gods are the same. Even if there are so many Gods like Trinity Shiva,Vishnu and Brahma, the core of the Hinduism says that all these Gods are the same. Krishna,Rama, Durga, Ganesha,etc and the number is lot more in the list of Gods. But see what Vedas says,
The most important texts in Hinduism,4 veda's mahavakyas(ultimate messages) are the following
1.Rig Veda - prajñānam Parabrahma - Wisdom/consciousness is the parabrahma(highest truth, not to be confused with 'Brahma' in Trinity)
2.Atharva Veda - ayam ātmā brahma- I am this Self is parabrahma
3.Sama Veda - tat tvam asi- You are that(parabrahma)
4.Yajur Veda - aham brahmāsmi- I am that (parabrahma)
All these creators in the world is considered as the part of one ultimate truth which can be called as a 'monotheistic GOD'. According to Hinduism, all these 33 million Gods are the same. Most of these Gods are the incarnations. Like Krishna and Rama are the incarnation of Lord Vishnu. Anyone can worship any of these Gods and get to the ultimate truth.
See a related question in Hinduism.SE here.
Also Hindus does not have strict restrictions in going to church or other temples like in Christianity or Islam. The reason is that Hindus believe that all Gods(in other religions too) are the part of the one ultimate truth or God. So isn't it the monotheism? Hindus who know the message of their culture know that everything is one.
Hinduism is one of the oldest religion, so while considering the core of message of the hinduism, it can be considered as the first monotheistic religion. It is way too older than Judaism, zourastrism or any other religions mentioned in other answers.
Not a messenger did We send before thee without this inspiration sent by Us to him: that there is no god but I; therefore worship and serve Me. Quran (21:25)
And it was already revealed to you and to those before you that if you should associate [anything] with Allah , your work would surely become worthless, and you would surely be among the losers. Quran (39:65)
We sent Noah to his people. He said: "O my people! worship Allah! ye have no other god but Him. I fear for you the punishment of a dreadful day! Quran(7:59)
And [We sent] Abraham, when he said to his people, "Worship Allah and fear Him. That is best for you, if you should know. You only worship, besides Allah , idols, and you produce a falsehood. Indeed, those you worship besides Allah do not possess for you [the power of] provision. So seek from Allah provision and worship Him and be grateful to Him. To Him you will be returned." Quran(29:16-17)
They have certainly disbelieved who say, " Allah is the Messiah, the son of Mary" while the Messiah has said, "O Children of Israel, worship Allah , my Lord and your Lord." Indeed, he who associates others with Allah - Allah has forbidden him Paradise, and his refuge is the Fire. And there are not for the wrongdoers any helpers. Quran(5:72)
According to Islam all religions were originally monotheistic but people changed them. So to relate to your question it is probably a religion that disappeared from practice.
It is interesting to travel in time and space, exploring the source of first monotheistic religion... APEU ( as per evolving understanding) it seems, before the religion comes the language - vocabulary/ terms/associated comparisons/reflections and so on. What if one has not learnt about polytheism - this word doesnt exist in one's learning ? how would one experience it? when one acquires meaning /words discussion starts.. How about exploring what religion/ connectivity/code of conduct one has even before learning a language? Is not that vibratory/ resonating in all , the first monotheistic element common to all as a first religion? just sharing to better evolve with your participation.