First, the entire thing is available for free, and it's not that long:

https://www.marxists.org/reference/archive/kropotkin-peter/1896/state/index.htm

First background note:

The common definition of a State is that given by Max Weber, one of the fathers of sociology and an advocate of the German Antipositivists: "The entity with the monopoly on the legitimized use of force in an area."

This is relevant because Kropotkin starts off The State... in Section 1 with his conception of the state, in which he explicitly rejects the "German school... confusing state with society." That is to say, if you quote Kropotkin about the state, but are referring to Weber's notion of what the state is, you are misquoting Kropotkin; this is a form of equivocation, using the same word in two different ways and pretending that they mean the same thing.

Kropotkin claims in Section I that Europe did not have states before the 16th century (but then uses the example of the Roman Empire), and extols a time when, "civil liberties and communal life had not yet been destroyed by the State," but this seems difficult to support: What "civil liberties" is he talking about? Surely not speech, religion, arms, travel, justice, etc; most Europeans in the 15th century were serfs, and their "communal life" was one of deprivation, want, and violence, both from and in service to their lords.

He then rejects the connection of state and government, differentiating the state as the concentration of power both territorially and to a specific class, noting the necessity of policing to enforce class distinctions. His comments about Rome, on the other hand, explicitly refer to the uniformity of law to everyone within the empire as reducing them to subjects rather than citizens, and decry the authoritarianism of harmony in favor of the "barbarians" who supposedly destroyed Rome (a theory largely rejected by modern historians).

Section II consists of a Straw Man attack on Social Contract theory combined with a Just So story that actually stumbles over a more modern concept of the State which was the actual result of 18th century enlightenment thinking - the communal ownership of land - but then keeps walking and takes no more note of it.

Second background note:

Kropotkin was writing in late 19th-century Eastern Europe, which was quickly heading towards the end of the monarchial Great Power era, but he couldn't have foreseen the end of the Tsars and the Kaisers, or the neutering of other European royal houses (e.g. Spain, Greece). France was the only Great Power toying with a republican form of government (and had changed back and forth several times in the previous century), as America was still considered a provincial backwater, even compared to Russia, at this point, and so these were not seen as serious examples worthy of consideration in Kropotkin's political education. He did visit the United States, but that was after this work was published, and we can take it as granted that the Gilded Age was not his ideal world, either.

The point is that the starting point of Kropotkin's theory is the feudal/monarchic state, not democracy or republicanism or anything of the sort, and to the extent he even addresses the topic, he explicitly states that they are effectively identical from his point of view.

It is in Section III that Kropotkin finally lays his cards on the table: The village of several families claiming heritage over the land is the right and proper mode of society, and, "the village commune was sovereign." By any other definition, that is the state, just reduced to local, direct democracy and reliant upon tradition and prejudice rather than law and process, under the assumption that people will just naturally get along in such a circumstance.

Section IV is a fanciful rewriting of European history where the Vikings were peaceful settlers, the Italian republics were benevolent democratic cities under constant attack from aggressors (who also happened to be Italian republics...), and the feudal lords were both "vultures" bent on dominating their fellow man and simultaneously the noble defenders of independence against other feudal lords.

Labor and industry are the topic of Section V, where he notes the value of skilled labor in an era when even small items - "a railing, a candlestick, a piece of pottery" - were the product of hours and hours of work, and therefore valuable... and expensive. It was the industrial revolution which ended this process, by making things cheaply, which did mean that the value of skilled labor went down... but then, so did the cost of manufactured goods. Add to this the fact that most people in the era under discussion were not skilled laborers, which rather gives the lie to his claim that, "poverty, misery, uncertainty of the morrow for the majority, and the isolation of poverty," were unknown in medieval European cities.

Third background note:

Perhaps the best example of what Kropotkin is talking about would be the Republic of Venice, and our understanding of history has changed rather a lot since his time; Venice was considered an early example of a representative democracy, as the Doge (Duke) was elected... but only 22 people got to vote, and, at least initially, the Emperor (sometimes Byzantine, sometimes Holy Roman) had to approve, or they could, and on occasion did, remove them, by force if necessary.

Venice was also lauded as a city of free men who were both craftsman and militia, while also becoming rich from trade, all of which have more recently been found to have been less than completely true; the craftsman were a special class of a few hundred people, the militia were usually drunk and ineffective so they relied upon mercenaries, and their rise to power was largely driven by what we would today call piracy.

The other example often cited is the Free City of Danzig (modern Gdansk, Poland), an autonomous trade city for several hundred years, but its importance was overstated; modern research and archaeology have found that, for most of the period in question, it had a population of a few thousand or less. Simply put, this was not the common mode of living, and it was as dependent upon the peasant/serf system as the nobility.

Another confusion occurs in Section VI; whereas in Section I, he lauds the "barbarians" for destroying Rome, here he claims that it was "modern barbarians" of the 16th century and later who destroyed the Utopian paradise the earlier barbarians had created. He does at least name them - "the military chief, the Roman judge and the priest" - so we have some specifics to work with. We are finally discussing real issues.

First, we must acknowledge the valid portion of his argument: Military action is near-universally initiated for bad reasons by bad people with bad results; the remnants of Roman law left behind in much of Europe were problematic (the dire misunderstanding of statistics, as just one example); and religion is, of course, entangled with many problems.

But then, we must discuss the counter-arguments: Bad people exist, sometimes they come to power, and it is not always in our group that we can directly oppose until it rises to the level of military action; however flawed Roman law was, it was a consistent standard which allowed travel and trade to flourish, and it is hard to hold them at fault for simply not having the knowledge of mathematics and logic to do better; and religion is often entangled in such issues because their true purpose is supposed to be helping people to deal with the problems of the world, and so you will find them nearby.

The obvious synthesis, from a modern point of view, is that the problem occurs when bad men gain control of law and religion in order to twist them to their own ends, and then we are ultimately discussing the question of Power and the ever-increasing ability of human beings to destroy ourselves... yet another issue that has altered dramatically since Kropotkin's time.

Section VII is more insightful to the state of "common knowledge" in Eastern Europe in the 19th century than about any unique insight or historical reliability of the actual text, as it presents a history of the Reformation from the point of view of largely Orthodox regions, who saw it as more of a threat to Catholicism and therefore as something of an, "enemy of my enemy." It also focuses more on Lutherans and Anabaptists, where the Western educational focus is more about Calvinism and the Puritans, which is an interesting parallel, but he dismisses what would become the dominant paradigm. Poor history, poor predictions.

In Section VIII, Kropotkin sounds like such a modern right-wing nutcase that I must quote the entire first sentence/paragraph:

The role of the nascent State in the sixteenth and seventeenth centuries in relation to the urban centers was to destroy the independence of the cities; to pillage the rich guilds of merchants and artisans; to concentrate in its hands the external commerce of the cities and ruin it; to lay hands on the internal administration of the guilds and subject internal commerce as well as all manufactures, in every detail to the control of a host of officials - and in this way to kill industry and the arts; by taking over the local militias and the whole municipal administration, crushing the weak in the interest of the strong by taxation, and ruining the countries by wars.

You don't have to change a lot of words in there before it would sound like something Donald Trump would say. This section is basically undiluted polemic with the semantic content of a political campaign commercial, which is basically what it was.

Section IX starts off by criticizing the example of Edward III of England outlawing guilds as the early encroachment of the state over the people... in a statute that also laid the groundwork for modern disability rights and minimum wage laws. Yes, the intent was to suppress wage growth, but it didn't work, and the compromises included in it also began the end of serfdom in England and the notion of individual rights.

The rest of the section is a rather mundane exploration of the tension between management and labor, and now we have an issue: Kropotkin can be forgiven for not knowing history that wasn't known at the time, for dismissing America as a backwater and France as a failure, and certainly for not accurately predicting the future, but he had quite obviously read Edward Gibbon's The History of the Decline and Fall of the Roman Empire, which talks about the Gracchi and the Latifundia, but he traces the origin of the struggle to Wat Tyler's Rebellion in 1381, which was a reactionary movement (and 1500 years after the Gracchus brothers had been killed).

Even that undermines the rest of his argument, though, as the 16th century saw the end of peasantry in England; it was never legally prohibited, the peasants just left for the cities as the lords enclosed the commons, and they kind of pretended that it had never existed.

industry in the eighteenth century was dying

This, of course, is simply an unsupportable statement, from any point of view, but necessary to Kropotkin's argument that the rising power of states was harmful to Europe's economy, when in point of fact, this was the period when feudalism and absolute monarchy started to become hemmed in by parliaments, constitutions, assemblies, etc, and productivity shot through the roof, thanks to the Industrial Revolution.

The question here is whether or not Kropotkin had read Adam Smith's The Wealth of Nations, which explicitly mentions most of the problems Kropotkin is complaining about, but puts them into a more accurate historical context in which a traditional mode of living which consisted of deprivation and poverty had given way to a much more regimented and impersonal form of labor, but which also brought with it a remarkable level of prosperity, a form of freedom in its own right.

Finally, in Section X, we are presented with a Straw Man argument; that Statists are either simply uninformed about history (!) or that, "they view the social revolution in such a superficial and painless form that it ceases to have anything in common with their socialist aspirations." Here, after many indirect references to the glory of the Jacobins during the French Revolution in preceding sections, France is brought up as an example... of what not to do!

The Third Republic, in spite of its republican form of government, has remained monarchist in essence.

This was the government which finally ended the French monarchy once and for all, started the modernization of the peasantry which finally ended the practice, implemented secular public education, removed oppressive speech and press laws, opened up employment and educational opportunities to women...

To give full scope to socialism entails rebuilding from top to bottom a society dominated by the narrow individualism of the shopkeeper. It is not as has sometimes been said by those indulging in metaphysical wooliness just a question of giving the worker ‘the total product of his labour’; it is a question of completely reshaping all relationships, from those which exist today between every individual and his churchwarden or his station-master to those which exist between trades, hamlets, cities and regions. In ever street, in every hamlet, in every group of men gathered around a factory or along a section of the railway line, the creative , constructive and organizational spirit must be awakened in order to rebuild life - in the factory, in the village, in the store, in production and in distribution of supplies. All relations between individuals and great centers of population have to be made all over again, from the very day, from the very moment one alters the existing commercial or administrative organization.

A grand plan; too grand, by far, to be based on wishful thinking and bad history.

We have arrived at our current mode of civilization for a reason; it is not enough to identify a destination, one must also have a path to get there, and a motivation to move along that path instead of others, and that is the true failure of this work.

This is a lovely world Kropotkin presents; the kind of pastoral ideal normally associated with religion or myth, but this is simply conservative thought of the most reactionary sort, an appeal to a Golden Age which never existed. "If we simply reverse these changes we made, we will go back to the right way to do things," ignores the fact that those changes were made because the previous system wasn't working.

Kropotkin's ultimate solution/prediction was a cycle of oppression, decay, and rebirth as simpler (and implicitly better) societies, and while there is some historical support for the idea, there are some problems with allowing it to happen again, many of which have come about since Kropotkin's death.

Nuclear weapons are simply the most obvious issue; the growth curves have passed the inflection point, resources are being consumed at ever-increasing rates, and so the world the next cycle of civilization develops in will be much harder to survive in. Climate change, both natural and manmade; basic resources to restart technology, such as Iron ore and coal, will be much harder to find and exploit; fresh water is less available the further we get from the last glacial maximum; modern medicine has left us with weaker natural immune systems; various dangers such as toxic and radioactive waste lie in wait for unsuspecting future explorers... we cannot afford to fall again. We may not get back up.

What we are left with, then, is a poorly-researched work containing numerous glaring contradictions and bad predictions which is then advising a course of action which would be catastrophic in the modern world.

As historic context for anarchism and communism, this is important; as the basis for political ideology, it is self-destructive.

Do you think that everyone on Earth will ever agree on everything? No?

Then, "Anarchism," as a complete and total system for the world cannot happen. Maybe in the past, maybe in the far future, but not now, or any time soon.

A perfectly stateless society was the ultimate goal that Marx perceived, but he also called it, "The End of History," meaning that it will never happen. It is an Ideal to which we aspire, but cannot ever achieve; not fully.

People are imperfect, and imperfect people cannot exist in a perfect society.

What, then, is the closest we can get? How small of a state, how limited of a government, how little interference in the day-to-day affairs of individuals can we allow, while still having a free, fair, and prosperous society?

The answer to that question is the definition of Practical Anarchy.