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This thesis describes a novel approach to the evolution of Modular Artificial Neural Networks. Standard Evolutionary Algorithms, used in this application include: Genetic Algorithms, Evolutionary Strategies, Evolutionary Programming and Genetic Programming; however, these often fail in the evolution of complex systems, particularly when such systems involve multi-domain sensory information which interacts in complex ways with system outputs. The aim in this work is to produce an evolutionary method that allows the structure of the network to evolve from simple to complex as it interacts with a dynamic environment. This new algorithm is therefore based on Incremental Evolution. A simulated model of a legged robot was used as a test-bed for the approach. The algorithm starts with a simple robotic body plan. This then grows incrementally in complexity along with its controlling neural network and the environment it reacts with. The network grows by adding modules to its structure - so the technique may also be termed a Growth Algorithm. Experiments are presented showing the successful evolution of multi-legged gaits and a simple vision system. These are then integrated together to form a complete robotic system. The possibility of the evolution of complex systems is one advantage of the algorithm and it is argued that it represents a possible path towards more advanced artificial intelligence. Applications in Electronics, Computer Science, Mechanical Engineering and Aerospace are also discussed.