José Antonio Ezquerro is Professor at the Department of Mathematics and Computation at the University of La Rioja in Spain.M. A. Hernández-Verón is Professor at the Department of Mathematics and Computation at the University of La Rioja in Spain.

“The text is easy to follow with full technical details given. Historical remarks are given throughout, which makes the reading especially interesting. The book also contains some numerical examples illustrating the theoretical analysis. It is a useful reference for researchers working on Newton method in Banach spaces.” (Bangti Jin, zbMATH 1376.65088, 2018)“This book is well written and will be useful to researchers interested in the theory of Newton’s method in Banach spaces. Two of its merits have to be mentioned explicitly: the authors offer all details for the proofs of all the results presented in the book, and, moreover, they also include significant material from their own results on the theory of Newton's method which were carried out over many years of research work.” (Vasile Berinde, Mathematical Reviews, March, 2018)

• The classic theory of Kantorovich.- Convergence conditions on the second derivative of the operator.- Convergence conditions on the k-th derivative of the operator.- Convergence conditions on the first derivative of the operator.

José Antonio Ezquerro is Professor at the Department of Mathematics and Computation at the University of La Rioja in Spain.M. A. Hernández-Verón is Professor at the Department of Mathematics and Computation at the University of La Rioja in Spain.

“The text is easy to follow with full technical details given. Historical remarks are given throughout, which makes the reading especially interesting. The book also contains some numerical examples illustrating the theoretical analysis. It is a useful reference for researchers working on Newton method in Banach spaces.” (Bangti Jin, zbMATH 1376.65088, 2018)“This book is well written and will be useful to researchers interested in the theory of Newton’s method in Banach spaces. Two of its merits have to be mentioned explicitly: the authors offer all details for the proofs of all the results presented in the book, and, moreover, they also include significant material from their own results on the theory of Newton's method which were carried out over many years of research work.” (Vasile Berinde, Mathematical Reviews, March, 2018)

• The classic theory of Kantorovich.- Convergence conditions on the second derivative of the operator.- Convergence conditions on the k-th derivative of the operator.- Convergence conditions on the first derivative of the operator.