It's Steffi Graf - she has won 22 Grand Slam singles titles, including the Golden Slam (all four Grand Slams in a year + the Olympic Gold Medal in singles, in 1988). Martina Navaratilova has won the most number of doubles Grand Slam titles. She is also the leading winner of overall Grand Slam titles.
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Steffi Graf was the first (and only) woman to win the Golden Slam of tennis in singles. She did it in 1988.
May Sutton Brandy became the first American woman to win the ladies singles tennis championship at Wimbledon in 1905.