A World History of Photography by Naomi Rosenblum (4th ed.) is another great choice for learning about the history of photography, particularly if you have specific areas of photography that you are most interested in.
The chapters of the book are broken down into chronological timeframes, but are also arranged thematically. An in-depth chapter about portraits 1839-1890 is followed by one on landscape and architecture during the same period, then documentation of objects and events, then art. As the book continues, thematic subjects are examined again in later timeframes.
The advantage to this arrangement is that you can settle in with a topic you are most interested in learning about and follow the history from that perspective. The disadvantage is there is less interweaving of the topics than in Photography: A Cultural History by Mary Warner Marien. Currently, you can pick up a used fourth edition of A World History of Photography for around $22 on AbeBooks. A new paperback copy lists for $60.