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Aside from trying to mimic the small yet powerful actuators and sensing systems that animals employ while running, understanding and implementing the control mechanisms that animals use to robustly negotiate uneven terrain at high speeds remains an unsolved problem. The objective of this dissertation is to make a significant contribution toward the development of a controller for the high-speed quadruped trot over uneven terrain. The trot was chosen because of its energy efficiency over a wide range of running speeds and its widespread use in nature. To this end, this dissertation 1) presents a fuzzy control strategy that manages the complex coupling between system inputs and body state to successfully track forward velocity and heading in a trot at high speeds and over uneven terrain, and 2) introduces a method for redistributing the leg forces during the support period to stabilize the body's tilt motion without overpowering or significantly disturbing the passive dynamics of a biomimetic trot. The controller stabilizes a 3D trot in simulation at 5.25 m/s, which is above the target speed of 3.90 m/s at which an animal of its mass would be expected to transition to its higher-speed gait, the gallop. The preferred trotting speed of a quadruped with this mass is 2.85 m/s. The quadruped can turn at 30 deg/s when running at this speed, and can maneuver over uneven terrain at 4.25 m/s. This work resulted in the first published report of quadruped heading control when running at such high speeds and is the first reported control of high-speed running over uneven terrain. The controller incorporates principles of the SLIP (spring-loaded inverted pendulum) model and the idea that animals redistribute vertical impulses during stance to stabilize pitch. The SLIP model is a simple spring-mass system that produces behavior similar to that observed in four-legged trotters and two-legged runners. Force redistribution is the process of altering the large leg forces that naturally occur during running to control selected body motions without significantly affecting others.