"Western Civilization: Ideas, Politics and Society, Volume 11" presents a comprehensive, textbook account of the history of Western civilization. Of course you'd need to supplement that with other regions in the world to get a fuller, world picture. I have a good title that does give such a full world account but I'm too lazy to get off the couch at the moment to check.

Eric Hobsbawm published a lot about the "long 19th century" and is quite famous for that. "The Age of Extremes" is focused on the 20th century. I enjoyed his work most of the time, even though Hobsbawm was a Marxist and has a certain political point of view, of course. But he was also a talented writer, so he's actually fun and easy to read. His academic reputation is untouched from that.

Keep in mind that "World History" generally has a strong tendency to metanarratives of all kind, so it's highly recommended to read more than one historian / one book about a certain time period. It can be very interesting to combine plots and narratives.