Timothy Snyder summing up Russia’s relationship to NATO from 1999 to 2010:

The eastward enlargement of NATO in 1999 was not presented by Putin as a threat. Instead, he tried to recruit the United States or NATO to cooperate with Russia to address what he saw as common security problems. After the United States was attacked by Islamist terrorists in 2001, Putin offered to cooperate with NATO in territories that bordered Russia. Putin did not present the EU enlargement of 2004 as a threat. On the contrary, he spoke favorably that year of future EU membership for Ukraine. In 2008, Putin attended the NATO summit in Bucharest. In 2009, Medvedev allowed American aircraft to fly over Russia to supply troops in Afghanistan. In 2010, Russia’s ambassador to NATO, the radical nationalist Dmitry Rogozin, expressed his concern that NATO would leave Afghanistan. Rogozin complained of NATO’s lack of fighting spirit, its “mood of capitulation.” He wanted NATO troops at Russia’s border.

Source: Snyder, The Road to Unfreedom: Russia, Europe, America (Tim Duggan Books, 2018), chap. 3.