The first Olympics that women could complete in in the modern era were held in the year 1900 in Paris, France. Twenty two women competed in two events (constituting 2% of all participants). This Olympics had humble beginnings. They did not have Opening or Closing ceremonies and they also did not give out medals, issuing bowls and mugs to the winners instead.
The two sports that women competed in were tennis and golf. There were a few others that they competed in with men but these were the only two sports that were women-only.
Tennis - Charlotte Cooper, from England, won in tennis. Previously, she was a three-time Wimbledon champion and won two times after the games (1901 and 1908). She became deaf at the age of 26 so all but one of her victories were as a deaf person. She was also notable because she was one of the few women that served overhand.
Golf - Margaret Ives Abbot won the first women’s Olympic golf match. She was an American who died in 1955 without ever realizing that her win was part of the Olympic games. The games were poorly organized and historical research did not establish that the game was part of the Olympic program until after her death. Her mother also competed in this golf match and finished seventh, making this the only time a mother and daughter have competed in the same games.