This chapter provides a comprehensive overview of edge detection techniques as fundamental tools for image analysis and computer vision. It begins by explaining the importance of edges as intensity discontinuities that define object boundaries and structural transitions, essential for segmentation and object recognition. The chapter explores the mathematical foundations of gradient-based detection, describing how first-order derivatives quantify local intensity variations through partial derivatives and gradient magnitude computation. Several classic operators are presented in detail, including Roberts, Prewitt, Sobel, and Compass (Kirsch) filters, each illustrating different approaches to estimating edge orientation and strength. The text also addresses second-derivative methods, focusing on the Laplacian operator, which detects edges via zero-crossings and enables isotropic edge localization. Furthermore, it introduces the concept of image sharpening by combining the original image with its Laplacian-filtered version to enhance detail and definition. Practical implementations using Python and OpenCV demonstrate step-by-step coding examples for gradient and Laplacian-based edge detection, thresholding, and visualization. Finally, the chapter concludes with an explanation of the Canny edge detector, emphasizing its multi-stage process for optimal edge localization, noise reduction, and one-pixel-width contour generation. Through mathematical derivation, algorithmic explanation, and practical coding exercises, this chapter offers a complete framework for understanding and applying edge and contour detection techniques in modern digital image processing.