For a highly readable intro to what happened in the late 80s through 90's I rec The Oligarchs by David Hoffman.
The Oligarchs by David Hoffman: https://www.amazon.ca/Oligarchs-Wealth-Power-New-Russia-ebook/dp/B005FYF4EI
Probably the best book on the subject.
You can also look up The Sale of the Century: https://www.amazon.ca/Sale-Century-Russias-Communism-Capitalism/dp/0812932153 which basically chronicles the wild 90s in Russia.
And you can go from there.
Not really. Most of the extreme concentrated wealth was accumulated in Russia in the 1990's during the corrupt privatisation process - during the infamous loan for shares scheme, where connected businessmen were able to gain control over valuable state-owned assets (especially oil, gas, aluminium) by using loans from connected banks. Harvard University consultants, with funding from the US State Dept, helped design the scheme that directly contributed, in many respects, to the rise of the Oligarchs. This all happened under President Yeltsin. The entire Russia administration was deeply corrupt, which was then capitalised on by the US and other Western nations. The goal of the West was to transition Russia as quickly as possible to "capitalism" to ensure it didn't revert back to communism. But there was a price to be paid for that rushed, deeply corrupt transition, which we are paying for now.
The later part of the 90's was a disaster for the Russian people economically speaking. By 1998, inflation reached nearly 90% and people lost their life savings. The IMF and World Bank had flooded Russia with debt - much of which (tens of billions of dollars) was then secreted out of the country in elaborate money laundering operations. By the end of the 90's Russia was effectively owned and controlled by the "7 Bankers" (or Semibankirschina) Putin was then handpicked to succeed Yeltsin by the Oligarchs that then controlled Russia (in particular Boris Berezovsky). The Oligarchs effectively controlled all the media and thus they could play an instrumental role in ensuring Putin's election. But Putin turned out to be far less compliant than they anticipated. Almost immediately upon his ascension, Berezovsky had a falling out with Putin.
Between 2000 and 2004, it was a battle between Putin and his new found populist/nationalist position as President and the Oligarchs who had up until that point stripped billions out of Russia. By 2004 a tentative truce had been reached - the most powerful Oligarchs were gone, either in exile or in prison. And the remainder agreed to fall into line with Putin's new directives.
If you want a good insight into how Russia came to be dominated by the Oligarch class, highly recommend you read The Oligarchs by David Hoffman.
EDIT: i also highly recommend people read up more on the details of Harvard University's key role in the Russia Privatisation process, in particular Larry Summers, Andrei Shleifer and the Harvard Institute for International Development. It's incredibly scandalous.