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This book deals with the new class of one-dimensional variational problems - the problems with branching solutions. Instead of extreme curves (mappings of a segment to a manifold) we investigate extreme networks, which are mappings of graphs (one-dimensional cell complexes) to a manifold. Various applications of the approach are presented, such as several generalizations of the famous Steiner problem of finding the shortest network spanning given points of the plane. Contents: Preliminary Results; Networks Extremality Criteria; Linear Networks in R N; Extremals of Length Type Functionals: The

Extremal problems (Mathematics) --- Steiner systems. --- Networks, Steiner --- Steiner networks --- Steiner triple systems --- Systems, Steiner --- Triple systems, Steiner --- Block designs --- Graph theory --- Problems, Extremal (Mathematics) --- Calculus of variations --- Geometric function theory --- Maxima and minima --- Extremal problems

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