August Comte (1798-1857) was a French philosopher who is widely credited with the coinage of the term sociology. His reliance on positivism, rejection of organized religion, and an emphasis on science and 'indoctrination' effectively influenced the future of the scientific study of human societies and how they function. While he was supposedly self-centered and egocentric, he nonetheless believed that we could understand society as a whole, objectively, and establish a 'new world order' that would essentially establish a peak of human achievement.
Comte's Early Life
August Comte was born in 1798 in Montpilier, France, into a Roman-Catholic family during the time of republicanism and skepticism. At an early age, Comte rectified these two viewpoints early by quickly rejecting his religion and the current royalist regime at the time, in favor of democracy/republicanism and secularization. This was after the occurrence of the French revolution. He went to a school called the École Polytechnique, a school in Paris that was intended for military engineers but eventually branched out to the sciences as well. Comte moved to Paris while he was there, and made a living from teaching mathematics and doing journalism.
He read a lot of philosophy and history, being influenced by writers like Montesquieu, A.R.J. Turgot, and Joseph de Maistre: all people that influenced his framework for his studies. Stemming from this, Comte then made a solid effort to attempt to find patterns in society itself to establish social 'truths', and more accurately, some sort of absolute social order that is omnipresent throughout human civilization. In addition, being influenced more by Henri de Saint-Simon, the founder of socialism, he was also able to identify the importance of economic regulation within a society(in contrast to cultural markers that are commonly mentioned in the conversation about what makes a society.) While they worked together for a while, their ideological stances diverged and Comte would go on to hold his own lectures about positivism, suffer a nervous breakdown, and came back for more by lecturing the shit out of the Royal Athenaeum in 1830.
He would then go on to tutor at his old school, the Polytechnique, and subsequently get booted out of the faculty for disagreements with the directors, and instead received support from English and French freelance financing. He would marry, and divorce, marry again, only to have his second wife die of tuberculosis. This experience would directly influence his works on women in regards to his positivism. After more of his friends died, he would dedicate his works on positivism to them, and finish his formulation of this kinda neat thing he coined 'sociology'. He had an emphasis on the social workings of morality and moral actions, specifically in how they create and influence a society to act a certain way as a whole.
The bastard died of cancer in 1857, where he couldn't defeat death in a deathmatch Thunderdome. 
Positivism and the three stages
What one thinks of positivism is not entirely what August Comte meant when he mentions the word 'positivism'. While it shares a lot of characteristics with what we think of it today, such as the presupposition of fact being the object of knowledge or that philosophy does not possess a different method than science, Comte's positivism also included some caveats in addition that you may or may not agree with, such as that all knowledge acquired from science must be useful in social engineering, and that all studies of science operate under the same style of study, where the only thing that differs is the subject matter that is being studied. In a sense, he claimed that positivism is the underlying philosophy behind scientific knowledge, with the assumption that it is the most effective way of understanding the world around us, and applied that as a sort of metastatement about all previously and future existing sciences in the course of human study.
The Three Stages Theory of Society Development
Because of his stance on positivism and its relation to the supernatural(namely that you shouldn't consider there to be one unless it's useful to know there is one) he established a theory, perhaps one of the first 'theories' of sociology, of how he thought all human societies would evolve and change over time to refine its understanding of the world around them.
The Theological Stage
The first step, the Theological stage, has a series of sub-steps that all transpire within the ideology of assigning explanations to things in the natural world around us. Where people start postulating ideas for what could cause certain things to happen in the world, there are steps that people go through to explain how they work.
The first sub-step is the belief in totemism, or assigning anthropomorphizations to non-living or non-conscious actors and objects. Stemming off of the human tendency to find agency where none exists, creating an evolutionary advantage, things that happen in the world around them are attributed with living being characteristics, notable examples including sacrificing things for the sun, personifying natural animals as deities, and in general treating commonplace objects as sacred intrinsically. Historically, this lines up because ancient religions are identified as a form of totemism, with evidence of people worshipping animals and existing objects as literal deities, rather than meaningful representations of deities that are not directly seen.
The second sub-step in the Theological stage is polytheism, which you could say is the mid point between totemism and monotheism. Instead of intrinsically believing that the objects that exist are in it of themselves powerful, they are now products of an intangible/otherworldy entity that is in charge of that said object. A common example is ancient Rome's pantheon of gods, all in charge of different strata of everyday life for the people during that time. You would, for instance, pray or offer credences to the specific god in charge of the thing that was related to your problem, in contrast to the previous offerings to the thing itself. This is notable from totemism, also, due to the development of representative items, such as priests for certain deities and the objects themselves representing the one singular deity.
The third and final sub-step is the monotheistic portion, in which all the gods in the previously poly-theistic pantheon were lumped together into one singular entity/character, simplifying the religious reasons for things happening to the core level it could be at. Indeed, instead of keeping track of which god does what, why not just create one single entity that does everything? Indeed, this is the part of this stage where 'intellect' was more heralded compared to the ad hoc worship of items or a pantheon of existence, where people 'figured out' it was just one god, acting multidimentionally. As more and more people accept a singular entity in contrast to multiple ones, there comes an easier consensus as to the nature of reality, and arrives a general sense of consistency for society as a whole.
A running theme throughout this stage is that the longer the religion exists, the more refined/basic it gets in its explanations for why things happen. Instead of imbuing each individual object with otherworldy power, there are instead multiple otherworldly entities represented by those things, and later just one single entity in charge of everything. In addition, throughout this stage, authority is usually garnered by people who have the 'best' explanations through the eyes of religion, namely, the kings and queens in place, the bishops, pope, and general clergy from the churches, and rich nobles that had wealth and power that was supposedly 'imbued or sanctioned from a higher power'.
The Metaphysical Stage
The second step, the Metaphysical stage, is a stage resting roughly between the 13-1800s, within an era of what one could call transitional. Instead of labeling a god figure as an actual being, it is instead treated more as an abstract concept underlying physical life. One very important hallmark of this region of thought is the idea that you reason things out, as characterized as the rise in philosophical thought, rather than simply sticking an explanation to something and being done with it. In comparison to the last stage, where perhaps a god being or some other anthropomorphization was applied to an object to explain how it works, people are now separating the two realms of reality and the metaphysical realm, talking about the connection between the two rather than assuming that they are one and the same.
During this era, the church remained powerful, but another entity that attained power during this time were those of the law-enforcing type, who enforced and created laws that other people would follow for extended periods of time. One crucial aspect of this portion of society is the existence of a near- or psuedo-totalitarian control from the government/whatever state entity existed at the time, whether it be a church or a kingdom. As during a majority of this time existed monarchies and extremely hierarchical definitions of social life, it follows that there was a relatively stable imbalance between the social groups.
The Positivist Stage
The third stage, the positivist stage, is the most extreme portion of time and also the most debatable one. Hallmarked by steps towards the scientific method, including observation, hypothesis, and conclusions, there was a slowly decreasing use in postulating explanations without evidence and an increase in citation-based reasoning. In a pure form, perhaps an Ideal Types of this stage, there would be absolutely no religious beliefs, superstition, or any sort of jumping to conclusions whatsoever. There would simply be reasons, observation, and no acceptance of any belief other than those that are empirically supported with evidence. A notable part of this stage is the vanishment of a god entity within the imagination, in particular.
One main stressor of this stage comparative to the other stages is an emphasis on the material world, and determining 'first causes' in the world for what happens and why it happens. Not necessarily some sort of cosmological argument, but rather in the form of finding as much information as you can in order to achieve a stance that reflects reality. In particular, he also goes on to say that all knowledge is human knowledge, and that by collecting all the information that we can, we as a society can roughly acknowledge what reflects 'true' reality.
There are some criticisms resting on these three stages, reflecting the assumptions and lines of thought that Comte stated to make his conclusion of his theory about human thought. One such criticism is that Comte has perhaps limited himself to three modes of thinking, disregarding that there may be a possible fourth stage, titled by Bogardus as socialized thinking, where people go beyond what is empirically true about reality and address the possible hierarchies and establishments of human society itself, and how it should run in the first place. Questions of hierarchy, bureaucracy, and what people 'should' do would probably rest under this mode of thought.
Another criticism that exists is one that is slightly more obvious, in that throughout history it was not necessarily a clear progression of all three stages. Perhaps this is due to the variation in human activity throughout socio-history, but the fact still stands that there are some things in our world, such as hard sciences like biology or chemistry, that are regarded with positivist ideals, while others, such as abiogenesis or cosmology, can be squarely within the realm of theology. In addition to areas of thought differing in regards to the standards of information, it also depends on geography and ethnoscapes, specifically the people that live in that area and what their common belief is. It's no secret that different parts of the world are disproportionately uneducated or in poverty, and that reflects on how they think. Even within a single individual could it be possible to find all three stages characterized in different modes of thought.
A final criticisms to note in this page is one of which may not have as many merits as the prior two, which is characterized by what C.E. Vaughn said: "But its foundation is purely negative and destructive. It is powerless to construct and when credited with the ability to do so, it brings forth nothing but Anarchism and bloodshed." Assuming that he is questioning the presuppositions that preclude the theoretical framework contributing to the three stages hypothesis, he most likely is trying to say that the way Comte describes society does not result in some sort of functional society. It seems like a watered down version of the first criticism that rests under an assumption itself that anarchy is necessarily a bad thing and that 'bloodshed'(which I assume he means violence) will be borne from.
(Author's note: A fairly weak criticism in my opinion but hey, its a criticism so evaluate it on your own merits.)
Comte's stance on religion
Reflecting his stance on the three stages, it's fairly clear that his stance on religion is that it's unneeded and that in place of supernatural thought, empirical facts should be taught in place to take advantage of that part of the human psyche. While he was surrounded by religion throughout his life, he saw the harm and groupthink that was borne from it and promptly rejected it, softly taking an anti-religion and anti-god stance in the form of a positivist style. While his views, like all other views, on life weren't perfect, he laid the groundwork for a different form of observation -> conclusion than was previously thought of, and formalized it with the label of 'sociology'. Over time, his works would influence those like Durkheim, Marx, and other scientists in the future regarding human society and thought.