The southernmost 809 mi / 1,302 km of the Continental Divide Trail (CDT) covers the stats of New Mexico. New Mexico can (somewhat accurately) be described as the “desert section” of the trail and the entire New Mexico CDT is above 4,000 ft / 1,220 m and more than 75% is above 6,000 ft / 1,830 m (with the high point appropriately found near the New Mexico/Colorado border).
Notable sections of New Mexico? The Bootheel, the Gila National Forest (which is actually an alternate route), the San Pedro Parks Wilderness, the Ignacio Chavez Special Management Area, El Malpais National Monument, and the Chama River Canyon Wilderness.
The photos below are in chronological/geographical order from south to north, and if you're really into photos of New Mexico you can check out the following posts as well: