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This 2003 book presents min-max methods through a study of the different faces of the celebrated Mountain Pass Theorem (MPT) of Ambrosetti and Rabinowitz. The reader is led from the most accessible results to the forefront of the theory, and at each step in this walk between the hills, the author presents the extensions and variants of the MPT in a complete and unified way. Coverage includes standard topics, but it also covers other topics covered nowhere else in book form: the non-smooth MPT; the geometrically constrained MPT; numerical approaches to the MPT; and even more exotic variants. Each chapter has a section with supplementary comments and bibliographical notes, and there is a rich bibliography and a detailed index to aid the reader. The book is suitable for researchers and graduate students. Nevertheless, the style and the choice of the material make it accessible to all newcomers to the field.

Mountain pass theorem. --- Critical point theory (Mathematical analysis) --- Hamiltonian systems. --- Variational principles. --- Variational inequalities (Mathematics) --- Maxima and minima. --- Nonsmooth optimization. --- Inequalities, Variational (Mathematics) --- Calculus of variations --- Differential inequalities --- Nonsmooth analysis --- Optimization, Nonsmooth --- Mathematical optimization --- Minima --- Mathematics --- Extremum principles --- Minimal principles --- Variation principles --- Hamiltonian dynamical systems --- Systems, Hamiltonian --- Differentiable dynamical systems --- Differential topology --- Global analysis (Mathematics) --- MPT (Mathematical analysis) --- Mountain pass theorem --- Hamiltonian systems --- Variational principles --- Variational inequalities --- Maxima and minima --- Nonsmooth optimization