I would not start with Huber's book, even with its 2009 revision, unless you possess strong mathematical background, i.e. measure theory and topology. The book by Maronna and Yohai entitled Robust Statistics: Theory and Methods is much more accessible for beginners and covers both univariate and multivariate theory, along with the computational aspects of the estimators (Chapter 9). So it is more modern in that respect.
Alternatively, if you find their book too easy but Huber's book still difficult there exists an intermediate alternative called Robust Statistics: The Approach Based on Influence Functions from Frank Hampel and co-authors (Hampel was the person who invented the influence function). The mathematical requirements are more modest and there is substantial motivation for the estimators.
All these books may be found in digital libraries but if you still have trouble obtaining pdf versions, you might want to try these notes, which are a fusion of all three books. You might also be pleased to know that all robust estimators exist in up-to-date R-packages, e.g. robustbase.