Partial least squares (PLS) has become an important statistical tool for modeling relations between sets of observed variables by means of latent variables especially for statistical problems dealing with high dimensional data sets. Despite of the fact that PLS handles multicollinearity problem, it fails to deal with data containing outliers since it is based on maximizing the sample covariance matrix between the response(s) and a set of explanatory variables, which is known to be sensitive to outliers. Existence of multicollinearity and outliers is no exception in real data sets, and it leads to a requirement of robust PLS methods in several application areas such as chemometrics. This book provides a detailed literature review on classical and robust PLS methods. The book introduces two new robust PLS methods that can be applied to regression (RoPLS) and classification (RoCPLS) problems. The content of the book should be especially useful for graduate students in statistics as a complementary material for classical multivariate data analysis courses and other researchers who can adopt the provided methodologies for real data analysis.