On June 16th, 1963 Soviet Cosmonaut Valentina Tereshkova became the first woman to travel into space. She spent 71 hours in space and completed 48 orbits before returning to earth. History.com notes that:
“The United States screened a group of female pilots in 1959 and 1960 for possible astronaut training but later decided to restrict astronaut qualification to men. The first American woman in space was astronaut and physicist Sally Ride, who served as mission specialist on a flight of the space shuttle Challenger in 1983.” http://www.history.com/this-day-in-history/first-woman-in-space
You can learn more about the women who almost became astronauts in Almost Astronauts: the Story of the Mercury 13 Women by Tanya Lee Stone. You can find this book in the Juvenile Nonfiction section at j629.45 STO.