Support Vector Machines (SVM) are a powerful classification algorithm used in machine learning and data analysis. The core idea behind SVM is to find the optimal hyperplane that separates data points of different classes in a high-dimensional space. This hyperplane is chosen to maximize the margin, or distance, between the data points of each class and the hyperplane, which helps in achieving better generalization and accuracy.

SVM can handle both linear and nonlinear classification problems. For linear classification, SVM finds a straight line (or hyperplane) that divides the classes. When dealing with nonlinear data, SVM employs a kernel trick to map the data into a higher-dimensional space where a linear separator can be found. Common kernel functions include polynomial, radial basis function (RBF), and sigmoid.

One of the strengths of SVM is its robustness against overfitting, especially in high-dimensional spaces. It is also effective in scenarios where the number of dimensions exceeds the number of samples. However, SVM can be computationally intensive and may require careful tuning of parameters to achieve optimal performance.