There are several synonyms for the phrase "woman of the world." Some of these include cosmopolitan, sophisticated, worldly-wise, experienced, and well-traveled. A woman of the world is someone who has a wide range of knowledge and experiences, often gained through exposure to different cultures and ways of life. She is someone who is comfortable navigating through a variety of social situations and can adapt to different environments. This phrase is commonly used as a compliment to describe a woman who is intelligent, cultured, and confident, and who can hold her own in any situation. These synonyms capture the essence of what it means to be a woman of the world.