Kernel methods in computational biology aim to provide a computational framework for biological research, integrating large datasets generated by high-throughput technologies and enabling the automatic generation of biological hypotheses. These methods are based on Mercer kernels and reproducing kernel Hilbert spaces (RKHS), which allow for the representation of various types of biological data in a unified framework. The paper discusses the mathematical theory of Mercer kernels, their properties, and the family of kernel methods they underpin. It also explores the application of kernel methods in biological systems, such as gene sets, and highlights their utility in statistical analysis and inference. Mercer kernels are symmetric and positive definite functions that can be associated with RKHS, enabling the representation of data in a Hilbert space. Kernel methods allow for computations in a high-dimensional space without explicitly mapping data, using the kernel trick. This approach is particularly useful for tasks like computing distances, performing principal component analysis (PCA), and canonical correlation analysis (CCA) in a Hilbert space. Support vector machines (SVM) are a key application of kernel methods, used for classification and regression tasks by finding optimal separating hyperplanes in a high-dimensional space. The paper also discusses the application of kernel methods to biological data, including protein sequences, gene expression profiles, and phylogenetic profiles. String kernels, such as the spectrum kernel and mismatch kernel, are used to compare gene sequences, while Fisher kernels and diffusion kernels are used to extract information from probabilistic models and graph structures. These methods enable the analysis of complex biological relationships and the integration of diverse data types. Kernel methods provide a powerful framework for analyzing biological data, enabling the extraction of meaningful insights from large and heterogeneous datasets. The paper emphasizes the importance of kernel operations and the combination of different kernels to incorporate multiple sources of information. Overall, kernel methods offer a versatile and theoretically sound approach to computational biology, facilitating the development of new algorithms and tools for biological research.Kernel methods in computational biology aim to provide a computational framework for biological research, integrating large datasets generated by high-throughput technologies and enabling the automatic generation of biological hypotheses. These methods are based on Mercer kernels and reproducing kernel Hilbert spaces (RKHS), which allow for the representation of various types of biological data in a unified framework. The paper discusses the mathematical theory of Mercer kernels, their properties, and the family of kernel methods they underpin. It also explores the application of kernel methods in biological systems, such as gene sets, and highlights their utility in statistical analysis and inference. Mercer kernels are symmetric and positive definite functions that can be associated with RKHS, enabling the representation of data in a Hilbert space. Kernel methods allow for computations in a high-dimensional space without explicitly mapping data, using the kernel trick. This approach is particularly useful for tasks like computing distances, performing principal component analysis (PCA), and canonical correlation analysis (CCA) in a Hilbert space. Support vector machines (SVM) are a key application of kernel methods, used for classification and regression tasks by finding optimal separating hyperplanes in a high-dimensional space. The paper also discusses the application of kernel methods to biological data, including protein sequences, gene expression profiles, and phylogenetic profiles. String kernels, such as the spectrum kernel and mismatch kernel, are used to compare gene sequences, while Fisher kernels and diffusion kernels are used to extract information from probabilistic models and graph structures. These methods enable the analysis of complex biological relationships and the integration of diverse data types. Kernel methods provide a powerful framework for analyzing biological data, enabling the extraction of meaningful insights from large and heterogeneous datasets. The paper emphasizes the importance of kernel operations and the combination of different kernels to incorporate multiple sources of information. Overall, kernel methods offer a versatile and theoretically sound approach to computational biology, facilitating the development of new algorithms and tools for biological research.