Wikipedia has a different version of Kondratieff's story than I have on this website (see the link How Elliott, Keynes, and Kondratieff fit together) that may well be more correct, and it is under the name Kondratiev, which is probably a more proper English spelling of his name in modern times. I will note that I have also seen his name spelled Kondratyev in the meantime, which may well be an even more proper English spelling of his name in the meantime. I have known about the Kondratieff wave since the 1980's, long before Wikipedia existed or the internet was publicly available, and the version of his story that I present on this website is the one that I remember, but the Wikipedia one is undoubtedly better-researched and probably has much more accurate information, now that the secretive Soviet Union has been collapsed for a long time and information about such things is probably much more readily available than it used to be. When I was studying the Kondratieff wave in the 1980's, the Soviet Union still very much existed, the internet was still years away from being publicly available to do research, and I was getting my information from other people by way of paper newsletters. Whichever version of the story is right, it does not change the basic point that I am trying to make on this website one bit.
As for the Kondratieff wave itself, Wikipedia has a description of the wave under the title Kondratiev wave. I agree with the first part of the description, and most of the rest of it, although I might add that, at times, it uses the terms in a slightly different way than I have been used to over the decades - I do not think that matters much, what matters is what is actually happening, and I provide a full description of that on this website - but I do not agree with their description of how deflation fits into the picture, which basically says that deflation is a thing of the past, and I do not think that expecting stagnation at this point is correct, I think the conditions for a deeper downturn are in place and I think that is what one should expect. This website goes into detail to provide a description of why deflation will still be a part of it and why one should expect a deep downturn. Wikipedia is written by volunteers and overseen by minders whose job it is to try to make sure that the information is both accurate and acceptable. I am quite sure my view will not be acceptable to the majority, at least not, at minimum, until my predictions that are contrary to what they say in the Wikipedia entry actually come true, and I therefore do not want to change the Wikipedia entry myself to include my view. I will leave my view of things on this website, where I control the information.
As noted at the top of the Wikipedia article about the Kondratieff wave itself, the theory is not accepted by current mainstream economics. Current mainstream economics, at least in America, is (neo)Keynesian, and this website discusses the issues around Keynesian and Austrian economics at some length - see directly-related links on this website that are explicitly labeled as such, as well as the comment about Austrian economics that is at the bottom of the link How Elliott, Keynes, and Kondratieff fit together. And in particular, as I note elsewhere on this website, the Kondratieff wave is compatible with Austrian economics, but not with Keynesian economics.
Also, as noted at the top of the Wikipedia article about economics that is referenced at the top of the Wikipedia article about the Kondratieff wave itself, "A primary stimulus for the development of modern economics was the desire to use an empirical approach more akin to the physical sciences." At the bottom of my link Keynesian economics vs. Austrian economics, I refute the idea in just a short paragraph (that is all it takes, in my opinion) that economics can be reduced to a set of equations. My basic premise is that economics is a social science, not a hard science, and people cannot be reduced to a set of equations.
Note: To get both of the Wikipedia articles at the same time, it is probably best to do a search on Nikolai Kondratiev.