Adaptive Computing, vs. Classical Computing, is emerging to be a field which is the culmination during the last 40 and more years of various scientific and technological areas, including cybernetics, neural networks, pattern recognition networks, learning machines, selfreproducing automata, genetic algorithms, fuzzy logics, probabilistic logics, chaos, electronics, optics, and quantum devices. This volume of "Critical Reviews on Adaptive Computing: Mathematics, Electronics, and Optics" is intended as a synergistic approach to this emerging field. There are many researchers in these areas working on important results. However, we have not seen a general effort to summarize and synthesize these results in theory as well as implementation. In order to reach a higher level of synergism, we propose Adaptive Computing as the field which comprises of the above mentioned computational paradigms and various realizations. The field should include both the Theory (or Mathematics) and the Implementation. Our emphasis is on the interplay of Theory and Implementation. The interplay, an adaptive process itself, of Theory and Implementation is the only "holistic" way to advance our understanding and realization of brain-like computation. We feel that a theory without implementation has the tendency to become unrealistic and "out-of-touch" with reality, while an implementation without theory runs the risk to be superficial and obsolete.