From the reviews: "This book is a collection of the work of the two authors over many years. ... The authors connect nicely the newest contributions and the 150 years of history of Darboux transformations and solvable potentials of the linear Schrodinger equation. ... The book can be recommended to graduate students ... ." (Dmitry E. Pelinovsky, Mathematical Reviews, Issue 2008 k) "The term 'dressing' generally implies a construction that contains a transformation from a simpler state to a more advanced state of a system. ... It provides new insight into this significant research area of great importance. ... The book can be of very great use to graduate students and professional mathematicians and physicists. ... It provides a good introduction to the dressing method, and it is definitely a good job." (Ma Wen-Xiu, Zentralblatt MATH, Vol. 1142, 2008)

• Mathematical preliminaries.- Factorization and classical Darboux transformations.- From elementary to twofold elementary Darboux transformation.- Dressing chain equations.- Dressing in 2+1 dimensions.- Applications of dressing to linear problems.- Important links.- Dressing via local Riemann–Hilbert problem.- Dressing via nonlocal Riemann–Hilbert problem.- Generating solutions via ? problem.