The study of patterns in data is as old as science. Consider，for example，the astronomical breakthroughs of Johannes Kepler formulated in his three famous laws of planetary motion. They can be viewed as relations that he detected in a large set of observational data compiled by Tycho Brahe. Equally the wish to automate the search for patterns is at least as old as computing. The problem has been attacked using methods of statistics，machine learning，data mining and many other branches of science and en-gineering. Pattern analysis deals with the problem of （automatically） detecting and characterising relations in data.Most statistical and machine learning meth-ods of pattern analysis assume that the data is in vectorial form and that the relations can be expressed as classification rules，regression functions orcluster structures，these approaches often go under the general heading of 'statistical pattern recognition'.cSyntactical' or 'structural pattern recogni-tion' represents an alternative approach that aims to detect rules among，for example，strings，often in the form of grammars or equivalent abstractions. The evolution of automated algorithms for pattern analysis has undergone three revolutions. In the 1960s efficient algorithms for detecting linear rela-tions within sets of vectors were introduced. Their computational and sta-tistical behaviour was also analysed. The Perceptron algorithm introduced in 1957 is one example. The question of how to detect nonlinear relations was posed as a major research goal at that time. Despite this developing algorithms with the same level of efficiency and statistical guarantees has proven an elusive target. In the mid 1980s the field of pattern analysis underwent a 'nonlinear revo-lution' with the almost simultaneous introduction of backpropagation multi layer neural networks and efficient decision tree learning algorithms. These approaches for the first time macle it possible to detect nonlinear patterns，albeit with heuristic algorithms and incomplete statistical analysis.The impact of the nonlinear revolution cannot be overemphasised： entire fields such as data mining and bioinformatics were enabled by it. These nonlinear algorithms，however，were based on gradient descent or greedy heuristics and so suffered from local minima. Since their statistical behaviour was not well understood，they also frequently suffered from overfitting. A third stage in the evolution of pattern analysis algorithms took place in the mid-1990s with the emergence of a new approach to pattern analy-sis known as kernel-based learning methods that finally enabled researchers to analyse nonlinear relations with the efficiency that had previously been reserved for linear algorithms.Furthermore advances in their statistical analysis made it possible to do so in high-dimensional feature spaces while avoiding the dangers of overfitting. From all points of view，computational，statistical and conceptual，the nonlinear pattern analysis algorithms devel-oped in this third generation are as efficient and as well founded as linear ones.The problems of local minima and overfitting that were typical of neural networks and decision trees have been overcome. At the same time，these methods have been proven very effective on non vectorial data，in this way creating a connection with other branches of pattern analysis. Kernel-based learning first appeared in the form of support vector ma-chines，a classification algorithm that overcame the computational and sta-tistical difficulties alluded to above. Soon，however，kernel-based algorithmsable to solve tasks other than classification were developed，making it in-creasingly clear that the approach represented a revolution in pattern analy-sis.Here was a whole new set of tools and techniques motivated by rigorous theoretical analyses and built with guarantees of computational efficiency. Furthermore，the approach is able to bridge the gaps that existed be-tween the different subdisciplines of pattern recognition. It provides a uni-fied framework to reason about and operate on data of all types be they vectorial，strings，or more complex objects，while enabling the analysis of a wide variety of patterns，including correlations，rankings，clusterings，etc. This book presents an overview of this new approach. We have attempted to condense into its chapters an intense decade of research generated by a new and thriving research community. Together its researchers have created a class of methods for pattern analysis，which has become an important part of the practitioner's toolkit.