Immanuel Kant was a key figure in the history of philosophy, instituting a "Copernican Revolution" in Western thought by showing that any philosophical analysis of reality is constrained by the structure of the human mind itself. Before proceeding in any philosophical analysis, therefore, one must first understand the limits and ways of thought that are necessitated by our mind. Any attempt to breach beyond these limits is futile and meaningless. The analysis and revelation of the precise constraints he termed 'transcendent' philosophy - transcendent to the main subject of philosophy, the one the philosopher wishes to explore.
For example, the aptly named Kant distinguished between phenomena, which are things as they appear to us, and noumena, things as they really are. He maintained that certain aspects of the phenomena were necessarily so by virtue of being perceived by humans. For example, he maintained that humans must necessarily perceive reality as extending in flat space and time. In modern terms, we would say humans are constructed by evolution to perceive of reality in terms of flat spacetime, even if they intellectually can tell that a curved spacetime is a more accurate description. In contrast, any speech of the noumena was completely without meaning. There is no way to examine any claim about noumena, such as whether spacetime really is curved (ignoring everything about modern physics). All we can speak of is whether we perceive spacetime to be flat or curved, we have no umediated access to spacetime itself, it is all mediated through the mind.
Kant is considered one of the greatest philosophers, and his work is studied extensively. Unfortunately, he was nearly incomprehensible even in his own time, and the passage of time (and translation) does not improve his clarity. His magnum opus, the Critique of Pure Reason was so opaque that he was forced to write An Introduction to Any Possible Metaphysics as a kind of shorthand version and introduction to the main text. Modern readers are advised to stay clear of this abominably complicated text as well, and instead read up on more modern accounts of Kant, that manage to convey his meaning without his obtuse style and also have the advantage of incorporating the thinking of later generations and critique of his work.
Kant's main works are the Critique of Pure Reason and the Critique of Practical Reason, really dense stuff about existence, knowledge and morality. He also wrote several other works, including Religion in the Light of Pure Reason where he argued for a religion that used the semantics of Christianity to appeal to the masses and convention, but had a layer of occult meaning intended for philosophers and those 'in the know' which was, essentially, atheistic.
He founded Kantianism, or the categorical imperative, a deontological moral philosophy which can be summed up in "act not unless you would have it be universal law without contradiction." This focuses on intentions rather than consequences, making it opposite to utilitarianism or consequentialism though it has largely fallen out in favor of these. A form of moral absolutism it nevertheless (arguably) does not require a divine source, but can be deduced by a priori logic as natural law-or not, depending on your views. Deontology's basis on duty, rather than teleology's consequences, makes it popular with modern libertarianism, as it means (what they view as) thefts are always wrong, and property rights always right, and Kant's notion of treating men as ends in themselves rather than means to an end deny justification for coercion. Of course, other libertarians support utilitarian morals.
He was also a real pissant, who was very rarely stable
On issues of race and gender, Kant was a man of his day. While many modern Kantians see the Categorical Imperative as clearly forbidding discrimination and bigotry based on race, gender and even sexual orientation, there is no evidence that Kant considered his prejudices as being in anyway contrary to his ethics. Perhaps this highlights the limitations of the Categorical Imperative as a means for arriving at maxims rather than a set of substantive moral rules.
By the standards of his time, however, Kant was a liberal. He favoured freedom of thought and conscience and constitutional government. He was often at odds with both Church and State, both for his support of limitations on the then absolute power of the monarchy and for his claims that ethics can be based on reason rather than revelation and that the existence of God could not be proven logically. Kant refuted many of the alleged proofs of God's existence which were then given a great deal of weight among Christian apologists. Most of these thoroughly debunked "proofs" are still listed as evidence for Christianity on Conservapedia. Kant settled on the moral argument for God's existence, since he felt it necessary to support his morality. In addition he staunchly defended the French Revolution, arguing that responsibility could not come before freedom; rather, people couldn't have responsibility without freedom.
As a form of moral absolutism, Kantianism is often identified with conservative and reactionary ideologies. However, Kant also has supporters on the other side of the spectrum. In his work The Open Society and Itss Enemies, philosopher of science and critic of religion Karl Popper unabashedly (but not uncriticially) identifies himself with the Kantian tradition while relentlessly attacking Aristotle, Plato, Friedrich Hegel and Karl Marx.
Ayn Rand had a habitual loathing for Kant whom she described as "the most evil man who ever lived." Rand saw his philosophy as the complete antithesis of her own. Ironically Kant and Rand aligned on certain points such as atheism, intellectual elitism and the supremacy of reason, though their reasons for valuing these principles and the application of their use were at odds. Rand viewed man as an end, incapable of further evolution. Leonard Peikoff a prominent Objectivist writes in his book, the DIM hypothesis. "In epistemology, Kant condemns man's consciousness as impotent to grasp real truth."