The soviet leader who began glasnost and perestroika was

mikhail gorbachev
joseph stalin
vladimir putin
v. i. lenin

 Mikhail Gorbachev

Explanation:

In March 1985, Mikhail Gorbachev proposed policies of perestroika (restructuring) and glasnost (openness) in the Soviet Union.  These seemed like policies that leaned in the direction of Western ways of economics and politics.  Perestroika meant allowing some measure of private enterprise in the Soviet Union.  Glasnost meant allowing a bit of freedom in regard to speech and publication.   But don't get the idea that Gorbachev was trying to get rid of the Soviet communist system.  He actually was trying to prop it up and preserve it, because it was starting to have many problems sustaining itself.  But in the end, opening things up a bit with perestroika and glasnost policies only pushed the USSR further in the direction of shedding the communist model under which it had lived for so long.