Kernel methods are a class of algorithms used in machine learning and statistics that enable the analysis of data in high-dimensional spaces. They work by applying a mathematical function, called a kernel, to transform the original data into a higher-dimensional space, making it easier to identify patterns and relationships. This transformation allows for more complex decision boundaries in classification tasks. One of the most popular kernel methods is the Support Vector Machine (SVM), which uses kernels to find the optimal hyperplane that separates different classes in the data. Other applications include Principal Component Analysis (PCA) and Gaussian Processes, which also benefit from the flexibility provided by kernel functions.