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This book systematically treats the theory of groups generated by a conjugacy class of subgroups, satisfying certain generational properties on pairs of subgroups. The theory of abstract root subgroups is an important tool to study and classify simple classical and Lie-type groups.

The theory of elliptic partial differential equations has undergone an important development over the last two centuries. The author discusses a priori estimates, normal solvability, the Fredholm property, the index of an elliptic operator, operators with a parameter, and nonlinear Fredholm operators.

After a discussion of the basic concepts in the theory of foliations in the first four chapters, the subject is narrowed down to Riemannian foliations on closed manifolds beginning with Chapter 5. Chapter 9 on Lie foliations is a prepa ration for the statement of Molino's Structure Theorem for Riemannian foliations in Chapter 10.

This volume presents the recent theory of function spaces, paying special attention to some recent developments related to neighboring areas such as numerics, signal processing, and fractal analysis.

This distinguishes it from the theory of nonlinear contraction semigroups whose basis is a nonlinear version of the Hille Yosida theorem: the Crandall-Liggett theorem. Thus the theory of nonlinear contraction semigroups does not apply to systems, in general, since they do not allow for a maximum principle.

From the reviews: "The text is almost self-contained and requires only an elementary knowledge of probability theory at the graduate level. Furthermore, some selected chapters can be used as sub-textbooks for advanced courses on stochastic processes, quantum theory and quantum chemistry."