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Efficient navigation in terms of travel time and energy dissipation is of crucial importance for biological micro-swimmers. The design of optimally navigating artificial swimmers also has potentially valuable applications such as targeted drug delivery, which has become an increasingly realistic perspective due to the recent progress in the experimental realization of controllable microswimmers able to perform nontrivial tasks. Despite recent theoretical progress, the field still faces open challenges, notably in describing navigation problems that take into account the complexities of the world of microswimmers.

This book presents a selection of works on the problem of optimal microswimmer navigation that represent a significant advance in this direction. The material in this book provides important insights into how efficient navigation may be achieved in the presence of curved space geometry, confining forces and flows, as well as thermal fluctuations. Finally, the energetic cost of navigation is addressed via a new formulation of the problem that accounts for the swimmer body geometry.