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The Soviet Union launched a series of six "manned" spacecraft beginning in the Spring of 1961. These flights demonstrated both the technological sophistication of the Soviet space program and accelerated developments in the United States. 

Vostok 1 - April 12, 1961 (First human in space)  
Vostok 2 - August 6, 1961  
Vostok 3 - August 11, 1962
(Launched on same day as Vostok 4)  
Vostok 4 - August 11, 1962 
(Flew within 3 miles of Vostok 5)  
Vostok 5 - June 14, 1963  
Vostok 6 - June 16, 1963 (First woman in space)