There are a few different territories that were gained by the Mexican-American war. The Treaty of Guadalupe Hidalgo granted the Mexican cession to the U.S. If by territories you mean states, the Mexican Cession included parts of states including California, Nevada, Utah, Arizona, New Mexico, and Wyoming. When Texas was completely annexed, it gave the U.S. all of Texas and parts of New Mexico, Oklahoma, and Kansas. The Gadsden Purchase also gave the U.S. parts of Southern Arizona and New Mexico including cities such as Tucson.
